Question

A spring has a stiffness of 100N/m. A mass of 3 kg was attached to the spring. The mass was pushed 10cm upward from the equilibrium position and was released from rest. After 5 seconds from release, determine the acceleration of the mass in m/s^2

Answer 1

Since Mass was displaced by 10 cm from mean position, it's amplitude of vibration A=0.1 m

Since body starts From extreme position,

The displacement of mass after time t is given by

$X=A\times cos(\sqrt{\frac{k}{m}}\times t)$

The acceleration of mass after time t is given as

$a=- \frac{k}{m}X=-\frac{k}{m}\times A\times cos(\sqrt{\frac{k}{m}}\times t)$

$a=-\frac{100}{3}\times 0.1\times cos(\sqrt{\frac{100}{3}}\times 5)=2.919\:m/s^2$