[go: up one dir, main page]
More Web Proxy on the site http://driver.im/

Presentation is loading. Please wait.

Presentation is loading. Please wait.

Physics 6B Oscillations Prepared by Vince Zaccone

Published bySharyl Fletcher Modified over 9 years ago

Similar presentations

Presentation on theme: "Physics 6B Oscillations Prepared by Vince Zaccone"— Presentation transcript:

1 Physics 6B Oscillations Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB Physics 6B Oscillations Prepared by Vince Zaccone

2 Definitions of quantities describing periodic motion
Period (T): time required for a motion to go through a complete cycle Frequency (f): number of oscillations per unit time Standard unit for frequency is Hertz (Hz) 1 Hz = 1 cycle/second Period and frequency are reciprocals Angular frequency: The amplitude (A) is the maximum displacement from equilibrium. Definitions of quantities describing periodic motion

3 Simple Harmonic Motion
A spring exerts a restoring force that is proportional to the displacement from equilibrium: Simple Harmonic Motion

4 Simple Harmonic Motion
Simple harmonic motion occurs when the restoring force is proportional to the displacement from equilibrium. Period of a mass on a spring: Total energy in simple harmonic motion: Simple Harmonic Motion

5 Equations for Simple Harmonic Motion
Position as a function of time: Velocity as a function of time: Acceleration as a function of time: Note that v(t) is just the derivative of x(t), and a(t) is the derivative of v(t) Equations for Simple Harmonic Motion

6 Energy in Simple Harmonic Motion
Potential energy as a function of time: Kinetic energy as a function of time: ½ kA2 _ Energy in Simple Harmonic Motion

7 a) how far is the spring compressed before the block comes to rest?
Example 1 A 0.98 kg block slides on a frictionless horizontal surface with speed 1.32m/s. The block encounters an unstretched spring with force constant 245N/m, as shown. a) how far is the spring compressed before the block comes to rest? b) how long is the block in contact with the spring before it comes to rest? c) how far is the spring compressed when the kinetic energy of the block is equal to the potential energy stored in the spring? Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB a) how far is the spring compressed before the block comes to rest

8 a) how far is the spring compressed before the block comes to rest?
Example 1 A 0.98 kg block slides on a frictionless horizontal surface with speed 1.32m/s. The block encounters an unstretched spring with force constant 245N/m, as shown. a) how far is the spring compressed before the block comes to rest? b) how long is the block in contact with the spring before it comes to rest? c) how far is the spring compressed when the kinetic energy of the block is equal to the potential energy stored in the spring? We can use energy conservation for the first part, setting the initial kinetic energy of the block equal to the final potential energy stored in the spring. Block at rest (spring fully compressed) Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB a) how far is the spring compressed before the block comes to rest

9 a) how far is the spring compressed before the block comes to rest?
Example 1 A 0.98 kg block slides on a frictionless horizontal surface with speed 1.32m/s. The block encounters an unstretched spring with force constant 245N/m, as shown. a) how far is the spring compressed before the block comes to rest? b) how long is the block in contact with the spring before it comes to rest? c) how far is the spring compressed when the kinetic energy of the block is equal to the potential energy stored in the spring? We can use energy conservation for the first part, setting the initial kinetic energy of the block equal to the final potential energy stored in the spring. Δx Block at rest (spring fully compressed) Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB a) how far is the spring compressed before the block comes to rest

10 a) how far is the spring compressed before the block comes to rest?
Example 1 A 0.98 kg block slides on a frictionless horizontal surface with speed 1.32m/s. The block encounters an unstretched spring with force constant 245N/m, as shown. a) how far is the spring compressed before the block comes to rest? b) how long is the block in contact with the spring before it comes to rest? c) how far is the spring compressed when the kinetic energy of the block is equal to the potential energy stored in the spring? We can use energy conservation for the first part, setting the initial kinetic energy of the block equal to the final potential energy stored in the spring. Δx Block at rest (spring fully compressed) Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB a) how far is the spring compressed before the block comes to rest

11 a) how far is the spring compressed before the block comes to rest?
Example 1 A 0.98 kg block slides on a frictionless horizontal surface with speed 1.32m/s. The block encounters an unstretched spring with force constant 245N/m, as shown. a) how far is the spring compressed before the block comes to rest? b) how long is the block in contact with the spring before it comes to rest? c) how far is the spring compressed when the kinetic energy of the block is equal to the potential energy stored in the spring? We can use energy conservation for the first part, setting the initial kinetic energy of the block equal to the final potential energy stored in the spring. Δx Block at rest (spring fully compressed) Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB a) how far is the spring compressed before the block comes to rest

12 a) how far is the spring compressed before the block comes to rest?
Example 1 A 0.98 kg block slides on a frictionless horizontal surface with speed 1.32m/s. The block encounters an unstretched spring with force constant 245N/m, as shown. a) how far is the spring compressed before the block comes to rest? b) how long is the block in contact with the spring before it comes to rest? c) how far is the spring compressed when the kinetic energy of the block is equal to the potential energy stored in the spring? v=1.32 For part b) we can use the formula for the period of oscillation of a mass-on-a-spring: Δx Block at rest (spring fully compressed) v=1.32 Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB a) how far is the spring compressed before the block comes to rest

13 a) how far is the spring compressed before the block comes to rest?
Example 1 A 0.98 kg block slides on a frictionless horizontal surface with speed 1.32m/s. The block encounters an unstretched spring with force constant 245N/m, as shown. a) how far is the spring compressed before the block comes to rest? b) how long is the block in contact with the spring before it comes to rest? c) how far is the spring compressed when the kinetic energy of the block is equal to the potential energy stored in the spring? v=1.32 For part b) we can use the formula for the period of oscillation of a mass-on-a-spring: Δx In this case we only want ¼ of the period. Block at rest (spring fully compressed) v=1.32 Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB a) how far is the spring compressed before the block comes to rest

14 a) how far is the spring compressed before the block comes to rest?
Example 1 A 0.98 kg block slides on a frictionless horizontal surface with speed 1.32m/s. The block encounters an unstretched spring with force constant 245N/m, as shown. a) how far is the spring compressed before the block comes to rest? b) how long is the block in contact with the spring before it comes to rest? c) how far is the spring compressed when the kinetic energy of the block is equal to the potential energy stored in the spring? v=1.32 Part c) is easiest to understand using energy. We know that Etotal = Kinetic + Potential. Δx Block at rest (spring fully compressed) v=1.32 Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB a) how far is the spring compressed before the block comes to rest

15 a) how far is the spring compressed before the block comes to rest?
Example 1 A 0.98 kg block slides on a frictionless horizontal surface with speed 1.32m/s. The block encounters an unstretched spring with force constant 245N/m, as shown. a) how far is the spring compressed before the block comes to rest? b) how long is the block in contact with the spring before it comes to rest? c) how far is the spring compressed when the kinetic energy of the block is equal to the potential energy stored in the spring? v=1.32 Part c) is easiest to understand using energy. We know that Etotal = Kinetic + Potential. We can also calculate the total energy from the given initial speed: Δx Block at rest (spring fully compressed) v=1.32 Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB a) how far is the spring compressed before the block comes to rest

16 a) how far is the spring compressed before the block comes to rest?
Example 1 A 0.98 kg block slides on a frictionless horizontal surface with speed 1.32m/s. The block encounters an unstretched spring with force constant 245N/m, as shown. a) how far is the spring compressed before the block comes to rest? b) how long is the block in contact with the spring before it comes to rest? c) how far is the spring compressed when the kinetic energy of the block is equal to the potential energy stored in the spring? v=1.32 Part c) is easiest to understand using energy. We know that Etotal = Kinetic + Potential. We can also calculate the total energy from the given initial speed: Δx Now we have to realize that when the kinetic and potential energies are equal, they are also each equal to half of the total energy. Block at rest (spring fully compressed) v=1.32 Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB a) how far is the spring compressed before the block comes to rest

17 a) how far is the spring compressed before the block comes to rest?
Example 1 A 0.98 kg block slides on a frictionless horizontal surface with speed 1.32m/s. The block encounters an unstretched spring with force constant 245N/m, as shown. a) how far is the spring compressed before the block comes to rest? b) how long is the block in contact with the spring before it comes to rest? c) how far is the spring compressed when the kinetic energy of the block is equal to the potential energy stored in the spring? v=1.32 Part c) is easiest to understand using energy. We know that Etotal = Kinetic + Potential. We can also calculate the total energy from the given initial speed: Δx Now we have to realize that when the kinetic and potential energies are equal, they are also each equal to half of the total energy. Since we want to find the compression distance, we should use the formula involving potential energy: Block at rest (spring fully compressed) v=1.32 Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB a) how far is the spring compressed before the block comes to rest

18 a) how far is the spring compressed before the block comes to rest?
Example 1 A 0.98 kg block slides on a frictionless horizontal surface with speed 1.32m/s. The block encounters an unstretched spring with force constant 245N/m, as shown. a) how far is the spring compressed before the block comes to rest? b) how long is the block in contact with the spring before it comes to rest? c) how far is the spring compressed when the kinetic energy of the block is equal to the potential energy stored in the spring? v=1.32 Part c) is easiest to understand using energy. We know that Etotal = Kinetic + Potential. We can also calculate the total energy from the given initial speed: Δx Now we can realize that when the kinetic and potential energies are equal, they are also each equal to half of the total energy. Since we want to find the compression distance, we should use the formula involving potential energy: Block at rest (spring fully compressed) v=1.32 Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB a) how far is the spring compressed before the block comes to rest

19 Mass-Spring Example Stop the Block Prepared by Vince Zaccone
For Campus Learning Assistance Services at UCSB Mass-Spring Example Stop the Block Prepared by Vince Zaccone

20 Example 2 A 0.260kg mass is attached to a vertical spring. When the mass is put into motion, its period is 1.12sec. How much does the mass stretch the spring when it is at rest in its equilibrium position? Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example 2

21 Example 2 A 0.260kg mass is attached to a vertical spring. When the mass is put into motion, its period is 1.12sec. How much does the mass stretch the spring when it is at rest in its equilibrium position? ? Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example 2

22 Example 2 A 0.260kg mass is attached to a vertical spring. When the mass is put into motion, its period is 1.12sec. How much does the mass stretch the spring when it is at rest in its equilibrium position? If we consider all the forces acting on the mass when it is hanging at rest we see that the weight must cancel the spring force. So if we can find the spring constant k, we can solve for x. ? kx mg Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example 2

23 Example 2 A 0.260kg mass is attached to a vertical spring. When the mass is put into motion, its period is 1.12sec. How much does the mass stretch the spring when it is at rest in its equilibrium position? If we consider all the forces acting on the mass when it is hanging at rest we see that the weight must cancel the spring force. So if we can find the spring constant k, we can solve for x. Use the formula for the period of a mass-spring system: ? kx mg Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example 2

24 Example 2 A 0.260kg mass is attached to a vertical spring. When the mass is put into motion, its period is 1.12sec. How much does the mass stretch the spring when it is at rest in its equilibrium position? If we consider all the forces acting on the mass when it is hanging at rest we see that the weight must cancel the spring force. So if we can find the spring constant k, we can solve for x. Use the formula for the period of a mass-spring system: ? kx Plugging in the given values we get mg Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example 2

25 Example 2 A 0.260kg mass is attached to a vertical spring. When the mass is put into motion, its period is 1.12sec. How much does the mass stretch the spring when it is at rest in its equilibrium position? If we consider all the forces acting on the mass when it is hanging at rest we see that the weight must cancel the spring force. So if we can find the spring constant k, we can solve for x. Use the formula for the period of a mass-spring system: ? kx Plugging in the given values we get mg Now we can use Fspring=weight: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example 2

26 Example 2 A 0.260kg mass is attached to a vertical spring. When the mass is put into motion, its period is 1.12sec. How much does the mass stretch the spring when it is at rest in its equilibrium position? If we consider all the forces acting on the mass when it is hanging at rest we see that the weight must cancel the spring force. So if we can find the spring constant k, we can solve for x. Use the formula for the period of a mass-spring system: ? kx Plugging in the given values we get mg Now we can use Fspring=weight: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example 2

27 The Simple Pendulum Looking at the forces on the pendulum bob, we see that the restoring force is proportional to sin θ, whereas the restoring force for a spring is proportional to the displacement (which is θ in this case). The Simple Pendulum

28 Period of a Pendulum A simple pendulum with small amplitude exhibits simple harmonic motion Period of a simple pendulum: Period of a physical pendulum: Period of a Pendulum A simple pendulum with small amplitude exhibits simple harmonic motion. Period of a simple pendulum:

29 You want to construct a simple pendulum with a 3
You want to construct a simple pendulum with a 3.25kg bob that will take 1.13sec to swing from a maximum angle of 9.5° to its lowest point after being released from rest. How long should this pendulum be? Here is a diagram of the pendulum. θ Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB You want to construct a simple pendulum with a 3

30 You want to construct a simple pendulum with a 3
You want to construct a simple pendulum with a 3.25kg bob that will take 1.13sec to swing from a maximum angle of 9.5° to its lowest point after being released from rest. How long should this pendulum be? Here is a diagram of the pendulum. We have a formula for the period of this pendulum: θ Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB You want to construct a simple pendulum with a 3

31 You want to construct a simple pendulum with a 3
You want to construct a simple pendulum with a 3.25kg bob that will take 1.13sec to swing from a maximum angle of 9.5° to its lowest point after being released from rest. How long should this pendulum be? Here is a diagram of the pendulum. We have a formula for the period of this pendulum: θ We can solve this for the length: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB You want to construct a simple pendulum with a 3

32 You want to construct a simple pendulum with a 3
You want to construct a simple pendulum with a 3.25kg bob that will take 1.13sec to swing from a maximum angle of 9.5° to its lowest point after being released from rest. How long should this pendulum be? Here is a diagram of the pendulum. We have a formula for the period of this pendulum: θ We can solve this for the length: What value should we use for the period? We are given a time of 1.13s to go from max angle to the lowest point. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB You want to construct a simple pendulum with a 3

33 You want to construct a simple pendulum with a 3
You want to construct a simple pendulum with a 3.25kg bob that will take 1.13sec to swing from a maximum angle of 9.5° to its lowest point after being released from rest. How long should this pendulum be? Here is a diagram of the pendulum. We have a formula for the period of this pendulum: θ We can solve this for the length: What value should we use for the period? We are given a time of 1.13s to go from max angle to the lowest point. This is only ¼ of a full cycle. So we multiply by 4: T = 4.52s Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB You want to construct a simple pendulum with a 3

34 You want to construct a simple pendulum with a 3
You want to construct a simple pendulum with a 3.25kg bob that will take 1.13sec to swing from a maximum angle of 9.5° to its lowest point after being released from rest. How long should this pendulum be? Here is a diagram of the pendulum. We have a formula for the period of this pendulum: θ We can solve this for the length: What value should we use for the period? We are given a time of 1.13s to go from max angle to the lowest point. This is only ¼ of a full cycle. So we multiply by 4: T = 4.52s Now we can plug in to get our answer: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB You want to construct a simple pendulum with a 3

35 Underdamped: the amplitude decreases exponentially with time:
Damped Oscillations Oscillations where there is a nonconservative (i.e. friction) force are called damped. Underdamped: the amplitude decreases exponentially with time: The frequency of oscillation is also affected. Critically damped: no oscillations; system relaxes back to equilibrium in minimum time Overdamped: also no oscillations, but slower than critical damping Underdamped: the amplitude decreases exponentially with time:

36 Damped Oscillations Damped Oscillations

37 An oscillating system may be driven by an external force
Driven Oscillations An oscillating system may be driven by an external force This force may replace energy lost to friction, or may cause the amplitude to increase greatly at resonance Resonance occurs when the driving frequency is equal to the natural frequency of the system An oscillating system may be driven by an external force

38 The Amplitude of the oscillation depends on the driving frequency.
Driven Oscillations The Amplitude of the oscillation depends on the driving frequency. 𝐴= 𝐹 𝑚 𝜔 0 2 − 𝜔 𝑏 2 𝜔 2 The Amplitude of the oscillation depends on the driving frequency.

Download ppt "Physics 6B Oscillations Prepared by Vince Zaccone"

Similar presentations

" alt="Physics January 26-27."> " class="uk-overlay-area">

Physics January
" alt="Physics 6B Oscillations Examples Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB."> " class="uk-overlay-area">

Physics 6B Oscillations Examples Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB.
" alt="Conservation of Energy Chapter 11 Conservation of Energy The Law of Conservation of Energy simply states that: 1.The energy of a system is constant."> " class="uk-overlay-area">

Conservation of Energy Chapter 11 Conservation of Energy The Law of Conservation of Energy simply states that: 1.The energy of a system is constant.
" alt="Kinematics of simple harmonic motion (SHM)"> " class="uk-overlay-area">

Kinematics of simple harmonic motion (SHM)
" alt="Horizontal Spring-Block Oscillators"> " class="uk-overlay-area">

Horizontal Spring-Block Oscillators
" alt="Chapter 5 Kinetic Energy"> " class="uk-overlay-area">

Chapter 5 Kinetic Energy
" alt="SHM -1."> " class="uk-overlay-area">

SHM -1.
" alt="18-2-20151FCI. Prof. Nabila.M.Hassan Faculty of Computer and Information Basic Science department 2013/2014 18-2-20152FCI."> " class="uk-overlay-area">

FCI. Prof. Nabila.M.Hassan Faculty of Computer and Information Basic Science department 2013/ FCI.
" alt="Adapted from Holt book on physics"> " class="uk-overlay-area">

Adapted from Holt book on physics
" alt="Problmes-1."> " class="uk-overlay-area">

Problmes-1.
" alt="Dr. Jie Zou PHY 1151G Department of Physics1 Chapter 13 Oscillations About Equilibrium (Cont.)"> " class="uk-overlay-area">

Dr. Jie Zou PHY 1151G Department of Physics1 Chapter 13 Oscillations About Equilibrium (Cont.)
" alt="Chapter 14 Oscillations Chapter Opener. Caption: An object attached to a coil spring can exhibit oscillatory motion. Many kinds of oscillatory motion are."> " class="uk-overlay-area">

Chapter 14 Oscillations Chapter Opener. Caption: An object attached to a coil spring can exhibit oscillatory motion. Many kinds of oscillatory motion are.
" alt="© 2007 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their."> " class="uk-overlay-area">

© 2007 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their.
" alt="Halliday/Resnick/Walker Fundamentals of Physics 8th edition"> " class="uk-overlay-area">

Halliday/Resnick/Walker Fundamentals of Physics 8th edition
" alt="Simple Harmonic Motion & Elasticity"> " class="uk-overlay-area">

Simple Harmonic Motion & Elasticity
" alt="Lecture 18 – Oscillations about Equilibrium"> " class="uk-overlay-area">

Lecture 18 – Oscillations about Equilibrium
" alt="Oscillations Phys101 Lectures 28, 29 Key points:"> " class="uk-overlay-area">

Oscillations Phys101 Lectures 28, 29 Key points:
" alt="13. Oscillatory Motion. Oscillatory Motion 3 If one displaces a system from a position of stable equilibrium the system will move back and forth, that."> " class="uk-overlay-area">

13. Oscillatory Motion. Oscillatory Motion 3 If one displaces a system from a position of stable equilibrium the system will move back and forth, that.
" alt="Simple Harmonic Motion"> " class="uk-overlay-area">

Simple Harmonic Motion
" alt="Periodic Motion - 1."> " class="uk-overlay-area">

Periodic Motion - 1.

Similar presentations

Ads by Google