A. T and v max both double. B. T remains the same and v max doubles.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

An object on the end of a spring is oscillating in simple harmonic motion. If the amplitude of oscillation is doubled, how does this affect the oscillation period T and the object’s maximum speed vmax?

A. T and vmax both double.

B. T remains the same and vmax doubles.

C. T and vmax both remain the same.

D. T doubles and vmax remains the same.

E. T remains the same and vmax increases by a factor of .

Q13.1


An object on the end of a spring is oscillating in simple harmonic motion. If the amplitude of oscillation is doubled, how does this affect the oscillation period T and the object’s maximum speed vmax?

A. T and vmax both double.

B. T remains the same and vmax doubles.

C. T and vmax both remain the same.

D. T doubles and vmax remains the same.

E. T remains the same and vmax increases by a factor of .

A13.1


Phase angle

Draw x(t) for a simple harmonic oscillator with A = 2m, T = 4s and the following three phase angles: f0 = 0, p/2, -p/2. Draw circular motion diagram to show initial conditions. Calculate the value of x(0) in the three situations to make sure your drawing is accurate.


This is an x-t graph for an object in simple harmonic motion.

A. t = T/4

B. t = T/2

C. t = 3T/4

D. t = T

Q13.2

At which of the following times does the object have the most negative velocity vx?



A. t = T/4

B. t = T/2

C. t = 3T/4

D. t = T

A13.2

At which of the following times does the object have the most negative velocity vx?



A. t = T/4

B. t = T/2

C. t = 3T/4

D. t = T

Q13.3

At which of the following times does the object have the most negative acceleration ax?



A. t = T/4

B. t = T/2

C. t = 3T/4

D. t = T

A13.3

At which of the following times does the object have the most negative acceleration ax?


SHO equations• A simple harmonic oscillator has an amplitude of 2 m and

oscillates with a period of 2s. What is its maximum velocity?• The SHO is started with a phase angle of f = p/2 with the same

period and amplitude. Draw the position vs. time graph.• The same SHO starts moving in the positive x direction starting

at x = 1m at t = 0s. What is the phase angle for this situation?


Energy in SHM• Energy is conserved during SHM and the forms (potential and

kinetic) interconvert as the position of the object in motion changes.


Energy in SHM II• Energy converts between kinetic and potential energy.


A. t = T/8 B. t = T/4

C. t = 3T/8 D. t = T/2

E. more than one of the above

This is an x-t graph for an object connected to a spring and moving in simple harmonic motion.

Q13.7

At which of the following times is the kinetic energy of the object the greatest?


A. t = T/8 B. t = T/4

C. t = 3T/8 D. t = T/2

E. more than one of the above

This is an x-t graph for an object connected to a spring and moving in simple harmonic motion.

A13.7

At which of the following times is the kinetic energy of the object the greatest?


Find velocity1) What is the velocity as a function of the position v(x) for a SHO glider with mass m and spring constant k?

Use conservation of energy

2) What is the maximum velocity of the glider? Compare this max velocity to your previous result to find w for a mass on a spring.


Vibrations of molecules • Two atoms separated by their internuclear distance r can be

pondered as two balls on a spring. The potential energy of such a model is constructed many different ways. The Leonard–Jones potential shown as Equation 13.25 is sketched in Figure 13.20 below. The atoms on a molecule vibrate as shown in Example 13.7.


Old carThe shock absorbers in my 1989 Mazda with mass 1000 kg are completely worn out (true). When a 980-N person climbs slowly into the car, the car sinks 2.8 cm. When the car with the person aboard hits a bump, the car starts oscillating in SHM. Find the period and frequency of oscillation.

How big of a bump (amplitude of oscillation) before you fly up out of your seat?


Damped oscillations II


Forced (driven) oscillations and resonance• A force applied “in synch” with a motion already in progress

will resonate and add energy to the oscillation (refer to Figure 13.28).

• A singer can shatter a glass with a pure tone in tune with the natural “ring” of a thin wine glass.


Forced (driven) oscillations and resonance II• The Tacoma Narrows Bridge suffered spectacular structural failure after absorbing too much resonant energy (refer to Figure 13.29).

A. T and v max both double. B. T remains the same and v max doubles.

Documents

Transcript of A. T and v max both double. B. T remains the same and v max doubles.