Question

A 2.5 kg object is attached to a spring (K=1500N/m) and is oscillating vertically. Calculate the period of the system. Also calculate the acceleration of the mass when spring is 2.3cm below its equilibrium position.

Answer 1

The period of a spring-mass system

$$T=2\pi\sqrt{m/k}=6.28\sqrt{2.5/1500}=0.26\:\rm s.$$

The acceleration of the mass

$$a=\frac{k\Delta x}{m}=\frac{1500\times 0.023}{2.5}=13.8\:\rm m/s^2.$$