A 4.0 kg mass is attached to a spring constant, k=2500N/m and isresting on a fri

Question

A 4.0 kg mass is attached to a spring constant, k=2500N/m and isresting on a frictionless horizontal surface. The spring isstretched by pulling on the mass until the amount of potentialenergy in the spring is 4.5 J. The block is then released andoscillates in simple harmonic motion.

1. What is the amplitude of the oscillation?

2. What is the maximum velocity of the block?

3. How long does it take for the block to go from maximum springlength to minimum spring length?

4. What is the velocity of the mass when it is 1.5 cm from thesprings equilibrium point?

Explanation / Answer

m = 4.0 kg, k = 2500 N/m, E = 4.5 J a) E = kA2/2, so A = (2E/k) = 6.0 cm b) = (k/m) = 25 rad/s vmax = A = 1.5 m/s c) period T = 2/ the required time t = T/2 = / = 0.126 s d) x = 1.5 cm kx2/2 + mv2/2 = E v = [(2E - kx2)/m] = 1.45 m/s

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