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Q.

Two simple harmonic oscillators with amplitudes in the ratio 1 : 2 are having the same total energy. The ratio of their frequencies is

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a

1: 4

b

1: 2

c

2: 1

d

4: 1

answer is C.

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Detailed Solution

$\begin{array}{l} T.E = \frac{1}{2} {mω}^{2} A^{2}; T^{E} E_{1} = T^{T} E_{2} \\ \frac{1}{2} {mω}_{1}^{2} A_{1}^{2} = \frac{1}{2} {mω}_{2}^{2} A_{2}^{2} \\ ω_{1}^{2} A_{1}^{2} = ω_{2}^{2} A_{2}^{2}; \frac{w_{1}}{w_{2}} = \frac{A_{2}}{A_{1}} = \frac{2}{1} \end{array}$

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