First slide

Simple harmonic motion

Question

A particle moves so that its acceleration a is given by $a = - b x$ , where $x$ is displacement from the equilibrium position and b is a constant. The period of oscillation is

Moderate

A

$2 π \sqrt{b}$
B

$\frac{2 π}{\sqrt{b}}$
C

$\frac{2 π}{b}$
D

$2 \sqrt{\frac{π}{b}}$

Solution

Condition for motion of a particle to be SHM is, acceleration of SHM is $a = - ω^{2} x$ , here $ω$ = angular velocity, x= displacement
Given equation , $a = - b x$
$∴ ω^{2} = b$
$ω = \sqrt{b}$ , time period is T
$\frac{2 π}{T} = \sqrt{b} \Rightarrow T = \frac{2 π}{\sqrt{b}}$

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