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Oscillations question bank (Physics)

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Q1.

The frequency of small oscillations of thin uniform vertical rod of mass $'m'$ and length $'l'$ hinged at point O with the help of two springs with spring constants $k_1$ and $k_2$, is

(A)

$\dfrac{1}{2\pi}\sqrt{\dfrac{(k_1 + k_2)}{m} + \dfrac{3g}{2l}}$

(B)

$\dfrac{1}{2\pi}\sqrt{\dfrac{3(k_1 + k_2)}{m} + \dfrac{3g}{2l}}$

(C)

$2\pi\sqrt{\dfrac{(k_1 + k_2)}{m} + \dfrac{g}{2l}}$

(D)

$2\pi\sqrt{\dfrac{(k_1 + k_2)}{3m} + \dfrac{2g}{3l}}$

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Q2.

A mass $0.4 \mathrm{~kg}$ performs S.H.M. with a frequency $\frac{16}{\pi} \mathrm{Hz}$. At a certain displacement it has kinetic energy $2 \mathrm{~J}$ and potential energy $1.2 \mathrm{~J}$. The amplitude of oscillation is

(A)

0.15 m

(B)

0.125 m

(C)

0.075 m

(D)

0.1 m

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