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Question

The energy of a particle executing simple harmonic motion is given by the equation $E = A x^{2} + B v^{2}$ where $x$ is the displacement from mean position $x = 0$ and $v$ is the velocity of the particle at $x$ . Find the amplitude of $S . H . M$ .

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Updated on : 2022-09-05

Solution

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$E = A x^{2} + B v^{2}$
As we know that at max amplitude, V $= 0$
$∴ E = A a^{2}$
Let a be amplitude
$∴ a^{2} = \frac{E}{A}$
$∣ a ∣ = \frac{E}{A _{1}}$ .

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