1. 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

2. A13.1
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

3. 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.

4. Q13.2
This is an x-t graph for an object in simple harmonic motion.
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

5. A13.2
This is an x-t graph for an object in simple harmonic motion.
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

6. Q13.3
This is an x-t graph for an object in simple harmonic motion.
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

7. A13.3
This is an x-t graph for an object in simple harmonic motion.
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

8. SHO equations
A simple harmonic oscillator has an amplitude of 2 m and oscillates with a period of 2 s. 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 velocity 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?

9. Energy in SHM
Mechanical energy (E = K + U) is conserved during SHM and the forms (potential and kinetic) interconvert as the position of the object in motion changes.

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

11. Q13.7
This is an x-t graph for an object connected to a spring and moving in simple harmonic motion.
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

12. A13.7
This is an x-t graph for an object connected to a spring and moving in simple harmonic motion.
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

13. Find velocity
1) What is the velocity as a function of the position v(x) for a SHO glider with mass m and spring constant k that was pulled by distance x = A and then released?
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.

14. Damped oscillations – Energy conservation?

15. 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.

16. Vibrations of molecules
Two atoms separated by their internuclear distance r can be pondered as two balls on a spring. The Leonard–Jones potential is shown below.
The wavenumber of the IR light is equal to f/c, where c = 3×108 m/s is the speed of light. The effective mass of CO is 14g/mol = 2.3×10-26kg/molecule
What is the frequency of oscillation for CO?
Find “spring constant” k of carbon monoxide from IR spectra.
Answer f = 6.3x10^13 Hz, k = m w^2 = kg/mol/6.02x10^23*(6.3x10^13 Hz)^2=92 N/m

17. Old car
The shock absorbers in my 1989 Mazda with mass 1000 kg were completely worn out (true). When a 980-N person climbed 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?

18. Forced (driven) oscillations and resonance II
The Tacoma Narrows Bridge suffered spectacular structural
failure after absorbing too much resonant energy