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

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

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

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  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 negativevelocityvx? 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 negativevelocityvx? 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 negativeaccelerationax? 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 negativeaccelerationax? 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 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?

  9. Energy in SHM • Energy 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? • 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. 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.

  15. Old car • The 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?

  16. Damped oscillations II

  17. 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.

  18. 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).

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