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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 Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 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 Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 2. 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. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 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 Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 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 Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 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 Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 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 Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 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? Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Energy in SHM • Energy is conserved during SHM and the forms (potential and kinetic) interconvert as the position of the object in motion changes. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Energy in SHM II • Energy converts between kinetic and potential energy. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 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 Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 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 Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 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. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 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. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 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? Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Damped oscillations II Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 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. Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley 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). Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley