First slide

Simple harmonic motion

Question

A particle in SHM is described by the displacement equation $x (t) = Acos (ωt + θ) .$ If the initial (t = 0) position of the particle is 1 cm and its initial velocity is $π$ cm/s, what is its amplitude? The angular frequency of the particle is ${πs}^{- 1}$

Moderate

A

1 cm
B

$\sqrt{2}$ cm
C

2 cm
D

2.5 cm

Solution

Given, $v = π cm / \sec,$ $x = 1 cm$ and $ω = {πs}^{- 1}$
using $v = ω \sqrt{a^{2} - x^{2}}$ $\Rightarrow π = π \sqrt{a^{2} - 1}$
$\Rightarrow 1 = a^{2} - 1 \Rightarrow a = \sqrt{2} cm$

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