Question

2. Following problem 1, the same spring-mass is oscillating, but the friction is involved. The spring-mass starts oscillating at the top so that its displacement function is x Ae-yt cos(wt)t is observed that after 5 oscillation, the amplitude of oscillations has dropped to three-quarter (three-fourth) of its initial value. (a) 2 pts] Estimate the value ofy. Also, how long does it take the amplitude to drop to one-quarter of initial value? 0 Co [2 pts] Estimate the value of damping constant b. How many times greater should the new damping constant be to create the critical damping mode for this spring-mass? (b) A block with a mass of 2.00 kg is attached to a spring, undergoing a horizontal simple harmonic motion with a frequency of 1.50 Hz. The initial speed of the block is 3.00 m/s when the spring is stretched by 50.0 cm. Letx-0 at the equilibrium position. Ignore friction for now. (a) [2 pts] Find the spring constant and the total energy of this object. 1. TE KE+PE - mv 31.2 J (b) 12 pts) Find the masimum displacement and masvimum speed of the motion. 203 =1,515 m lo alley C с 2010 Diablo (c) 12 pts) For the block, at what position x is the speed a minimum? At what position x is the acceleration a minimum (in magnitude)? Show your answers of x as numerical values. Be ready to explain in discussion.

Answer 1

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xH-0 hen o position e at t 6o th equahion hecome

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86 301 x 10 16.06 vec .. . takes 16-06 sec to drop the amplitude to one- quanten ob is initral value. The value o damping coutanl is given by b am 0 34520 N5m fon critcal dampi oriftal danpi 5) = 3R6991)-- 109.2 crmate Hu calping Mode