A 2.00 kg block hangs without vibrating at the end of a spring(k=500 N/m) that i

Question

A 2.00 kg block hangs without vibrating at the end of a spring(k=500 N/m) that is attached to the ceiling of an elevator car. Thecar is rising with an upward acceleration of g/3 when theacceleration suddenly ceases (at t=0). a.) What is the angularfrequency of oscillation of the block after the accelerationceases? b.) By what amount is the spring stretched during the timethat the elevator car is accelerating? This distance will be theamplitude of the ensuing oscillation of the block.

Explanation / Answer

m = 2.0 kg k = 500 N/m ay= g/3 w = (k/m) => (500/2) w = ? rad/s Now use sum of forces in the Fy. Fy = Fs - mg = may Fs = kx kx - mg = may   => kx = mg +may => kx = m ( g + ay) => x = m ( g + (g/3)) / k => x = m4g/3k x = 4 * (2.0 kg) * (9.8 m/s) / (3 * 500 N/m) x = ? m (change it intocm)

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