First slide

Simple harmonic motion

Question

The equation of motion of a particle executing simple harmonic motion is a $a + 16 π^{2} x = 0$ . In this equation, a is the linear acceleration in m/s² of the particle at a displacement x in meter. The time period in simple harmonic motion is

Moderate

A

$\frac{1}{4} \sec$
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 $ω = 4 π$
$and T = \frac{2 π}{ω} = \frac{2 π}{4 π} = \frac{1}{2} \sec$

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