An object of mass 0.2 kg executes simple harmonic motion along x axis with frequency of . At the position the object has kinetic energy 0.5 J and potential energy 0.4 J. The amplitude of oscillation is ________ cm.

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Solution

Q.
An object of mass 0.2 kg executes simple harmonic motion along x axis with frequency of $(\frac{25}{π}) H z$ . At the position $x = 0.04 m$ the object has kinetic energy 0.5 J and potential energy 0.4 J. The amplitude of oscillation is ________ cm. [2024]

Ans.
(6) $Total energy = K . E . + P . E .$

$x = 0.04 m,$ $T . E . = 0.5 + 0.4 = 0.9 J$

$\Rightarrow \frac{1}{2} \times 0.2 {(2 π \times \frac{25}{π})}^{2} \times A^{2} = 0.9$

$\Rightarrow A = 0.06 m = 6 c m$

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