First slide

Simple hormonic motion

Question

The equation of motion of a particle executing simple harmonic motion is $a + 16 π^{2} x = 0$ . In this equation, a is the linear acceleration in $m / s^{2}$ of the particle at a displacement x in meter. The time period in simple harmonic motion is:

Moderate

A

$\frac{3}{4} \sec$
B

$\frac{1}{2} \sec$
C

1 sec
D

2 sec

Solution

$a = - 16 π^{2} x$
Standard equation of SHM is:
$A = - ω^{2} x$
Hence, comparing two equations, we get,
$ω = 4 π$
$T = \frac{2 π}{ω}$ $= \frac{2 π}{4 π} = \frac{1}{2} \sec$

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