Question

VERTICAL SPRING

A spring of negligible mass, spring constant k = 89 N/m, and natural length l = 1.4 m is hanging vertically. This is shown in the left figure below where the spring is neither stretched nor compressed. In the central figure, a block of mass M = 2 kg is attached to the free end. When equilibrium is reached (the block is at rest), the length of the spring has increased by d1 with respect to l. We now lower the block by an additional d2 = 0.4 m as shown in the right figure below. At t=0 we release it (zero speed) and the block starts to oscillate. Take g=9.81 m/s2


(a) Find d1.


(b) What is the frequency (Hz) of the oscillations?


(c) What is the length of the spring when the block reaches its highest point during the oscillations?


(d) What is maximum speed of the block?