Question

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

Answer 1

amplitude = maximum displacement from the equilibrium position

A = δ₁ - δ₀ = 0.10 – 0.04 = 0.06 m.

(d) Initial velocity = 0 (given)

Initial acceleration = kδ_i -mg/m

= 500(0.1) - 2(10)/2

= 15 m/s² upward