Answer to Question #182163 in Mechanical Engineering for luke

Question

A spring has a stiffness of 100N/m. A mass of 4 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 the mean position, its amplitude of vibration A=0.1 m

Since the body starts From an 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

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

$a=-\frac{100}{4}\times 0.1\times cos(\sqrt{\frac{100}{4}}\times 5)=-2.478\:m/s^2$