In figure (12-E3) k = 100 N m^{-1}, M = 1 kg and F = 10 N. (a) Find the compression of the spring in the equilibrium position. (b) A sharp blow by some external agent imparts a speed of 2 m s^{-1} to the block towards left. Find the sum of the potential energy of the spring and the kinetic energy of the block at this instant. (c) Find the time period of the resulting simple harmonic motion. (d) Find the amplitude. (e) Write the potential energy of the spring when the block is at the left extreme. (f) Write the potential energy of the spring when the block is at the right extreme. The answers of (b), (e) and (f) are different. Explain why this does not violate the principle of conservation of energy.

Given

a) In the equilibrium position, compression

b) The blow parts speed of 2 m/s to the block towards left.

c)

d) Let the amplitude be x which means that the between the mean position and the extreme position. So, in the extreme position, compression of the spring is.

Since, in the SHM, the total energy remains constant.

e) Potential energy at the left extreme is given by

f) Potential energy at the right extreme is given by

The different values in (*b), (e), (f)* do not violate law of conservation of energy as the work is done by the external force.

1