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Standard XI
Physics
Simple Harmonic Motion
Question

A $$2\ kg$$ block hangs without vibrating at the bottom end of a spring with a force constant of $$800\ N/m$$. The top end of the spring is attached to the ceiling of an elevator car. The car is rising with an upwards acceleration of $$10\ m/s^{2}$$ when the acceleration suddenly ceases at time $$t=0$$ and the car moves upward with constant speed $$(g=10\ m/s^{2})$$
What is the angular frequency of oscillation of the block after the acceleration ceases?

A
$$20\ rad/s$$
B
$$32\ rad/s$$
C
$$10\sqrt{2}\ rad/s$$
D
$$20\sqrt{2}\ rad/s$$
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Solution
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Correct option is B. $$20\ rad/s$$
As elevator starts rising up with $$a=10\,m/s^2$$ pseudo force act on block.
$$F=ma$$ in downward direction.
Spring Force =$$Kx$$ in upward direction
angular frequency is given by
$$\omega=\sqrt{\dfrac{k}{m}}$$
$$\omega=\sqrt{\dfrac{800}{2}}$$
$$\omega=20\,rad/s$$

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