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At what displacement is the KE of a particle performing SHM of amplitude 10 cm, three times its PE ?

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15 cm

10cm

20cm

5 cm

answer is B.

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Detailed Solution

$\begin{array}{l} K.E = 3 (P.E) \\ \Rightarrow \frac{1}{2} m ω^{2} (A^{2} - y^{2}) = 3 \frac{1}{2} m ω^{2} y^{2} \\ A^{2} - y^{2} = 3 y^{2} \Rightarrow 4 y^{2} = A^{2} \\ y = A / 2 y = \frac{10}{2} = 5 cm \end{array}$

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