The spring mass system is shown in the figure. The spring stretches 2 cm from its free length when a force of 10 N is applied. This spring is stretched 10 cm from its free length, a body of mass m = 2kg attached to it and released from rest at time t = 0. Find

(a) the force constant of the spring.

(b) the time period and frequency of vibration

(c) the amplitude of vibration.

(d) the initial velocity and acceleration

(e) the maximum velocity and acceleration

(f) the spring force at the two extreme position of the body.

(g) the time taken by the body to move half way towards the equilibrium position from its initial position. Write the equation of motion of the body in the form x = A sin (*√* *ω*t + *ϕ*) where x is the displacement from the equilibrium position. Express the spring force as a function of time.