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Unformatted text preview: Le (tl8426) HW11 gentle (56245) 1 This printout should have 8 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points A simple harmonic oscillator has amplitude . 56 m and period 2 . 9 sec. What is the maximum acceleration? 1. . 0665874 m / s 2 2. 7 . 62342 m / s 2 3. . 418381 m / s 2 4. 2 . 62877 m / s 2 correct 5. 1 . 31438 m / s 2 6. . 193103 m / s 2 Explanation: Let : A = 0 . 56 m and T = 2 . 9 sec . For a simple harmonic oscillator, the dis placement is x = A cos parenleftbigg 2 T t + parenrightbigg , so the acceleration is a = d 2 x dt 2 = A parenleftbigg 2 T parenrightbigg 2 cos parenleftbigg 2 T t + parenrightbigg . Since 1 < cos < 1, the maximum acceler ation is A max = 4 2 A T 2 = 4 2 (0 . 56 m) (2 . 9 sec) 2 = 2 . 62877 m / s 2 . 002 10.0 points Simple harmonic motion can be described us ing the equation x = x m sin( t + ) . If x = initial position, v = initial velocity, then 1. tan = x v 2. tan = v x 3. tan = + v x 4. tan = + x v correct Explanation: x = x m sin( t + ) v = dx dt = x m cos( t + ) When t = 0, x = x m sin v = x m cos x m sin x m cos = x v tan = x v . 003 10.0 points A 54 kg person steps into a car of mass 2761 kg, causing it to sink 0 . 59 cm on its springs. Assuming no damping, with what fre quency will the car and passenger vibrate on the springs? The acceleration of gravity is 9 . 81 m / s 2 . Correct answer: 0 . 898848 Hz. Explanation: Let : m = 54 kg , M = 2761 kg , g = 9 . 81 m / s 2 , and x = 0 . 59 cm = 0 . 0059 m . Le (tl8426) HW11 gentle (56245) 2 The spring force is F = k x k = F x = mg x , where m is the persons mass....
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This note was uploaded on 12/05/2011 for the course PHY 301 taught by Professor Swinney during the Fall '07 term at University of Texas at Austin.
 Fall '07
 Swinney
 mechanics, Simple Harmonic Motion

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