Question

A 2.5 kg box rests atop a massive vertical spring with k=4250 N/m that has been compressed by 15cm from its equilibrum position.The box is released and leaves the pring when it reaches its equilibrum position. What is (a) the equilibrum position and (b) the maximum height the box reaches above its original position ?

Answer 1

a) At the equilibrium position Weight of the box is exactly balanced by the restoring force of the spring.

Thus   

If "x_o" is its equilibrium position then we'll have

  

Using given values in above,

(ANS)

Hence equilibrium length of spring, x_o= 0.576cm (ANS)

b). Initial Compression of the box= Maximum Amplitude of the oscillation when released.

Thus A= 15cm

Thus Maximum Height of the box from equilibrium position, H= A= 15cm

and Maximum Height of the box from original position,

     (ANS)