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HW11-solutions

# HW11-solutions - Le(tl8426 HW11 gentle(56245 1 This...

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Le (tl8426) – HW11 – gentle – (56245) 1 This print-out should have 8 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points A simple harmonic oscillator has amplitude 0 . 56 m and period 2 . 9 sec. What is the maximum acceleration? 1. 0 . 0665874 m / s 2 2. 7 . 62342 m / s 2 3. 0 . 418381 m / s 2 4. 2 . 62877 m / s 2 correct 5. 1 . 31438 m / s 2 6. 0 . 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 π T t + φ parenrightbigg , so the acceleration is a = d 2 x dt 2 = - A parenleftbigg 2 π T parenrightbigg 2 cos parenleftbigg 2 π T t + φ parenrightbigg . Since - 1 < cos α < 1, the maximum acceler- ation is A max = 4 π 2 A T 2 = 4 π 2 (0 . 56 m) (2 . 9 sec) 2 = 2 . 62877 m / s 2 . 002 10.0points Simple harmonic motion can be described us- ing the equation x = x m sin( ωt + φ ) . If x 0 = initial position, v 0 = initial velocity, then 1. tan φ = - ω x 0 v 0 2. tan φ = - v 0 ω x 0 3. tan φ = + v 0 ω x 0 4. tan φ = + ω x 0 v 0 correct Explanation: x = x m sin( ω t + φ ) v = d x dt = x m ω cos( ω t + φ ) When t = 0, x 0 = x m sin φ v 0 = x m ω cos φ x m sin φ x m ω cos φ = x 0 v 0 tan φ = ω x 0 v 0 . 003 10.0points 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 Δ x = 0 . 59 cm = 0 . 0059 m .

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Le (tl8426) – HW11 – gentle – (56245) 2 The spring force is F = k Δ x k = F Δ x = m g Δ x , where m is the person’s mass. The frequency is f = 1 2 π radicalbigg k m + M = 1 2 π radicalbigg m g ( m + M ) Δ x = 1 2 π radicalBigg (54 kg) (9 . 81 m / s 2 ) (54 kg + 2761 kg) (0 . 0059 m) = 0 . 898848 Hz . 004 10.0points A horizontal platform vibrates with simple harmonic motion in the horizontal direction with a period of 2 . 81 s. A body on the plat- form starts to slide when the amplitude of vibration reaches 0 . 438 m.
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HW11-solutions - Le(tl8426 HW11 gentle(56245 1 This...

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