Question

A $2kg$ block hangs without vibrating at the bottom end of a spring with a force constant of $400N/m$. The top end of the spring is attached to the ceiling of an elevator car. The car is rising with an upward acceleration of $5m/s^2$ when the acceleration suddenly ceases at time $t=0$ and the car moves upward with constant constant speed. $(g=10m/s^2)$. What is the angular frequency of oscillation of the block after the acceleration ceases?

Answer 1

As elevator gains acceleration, a downward pseudo force will start acting on it. Here acceleration is given to displace the body only so after ceasing this acceleration the body will start performing SHM.

$T=2\pi \sqrt{\frac{m}{K}}so,\omega =\sqrt{\frac{K}{m}}\omega =\sqrt{\frac{400}{2}}\omega =10\sqrt{2}rad/s$