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CGP EDU Academic Team
Published on: September 12, 2026
A particle in SHM is described by the displacement equation $x(t) = A \cos(\omega t + \theta).$ If the initial (t = 0) position of the particle is 1 cm and its initial velocity is $\pi$ cm/s, what is its amplitude? The angular frequency of the particle is $\pi s^{-1}$
Text Solution
Verified by ExpertsThe correct answer is:
B
Given, $x = 1 \mathrm{cm}$ and $\omega = \pi s^{-1}$
using $\mathbf{v} = \omega \sqrt{a^{2} - x^{2}}$ ⇒ ⇒ $\pi = \pi \sqrt{a^{2} - 1}$
$\Rightarrow 1 = A^{2} - 1 \Rightarrow A = \sqrt{2} \text{cm}.$
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