The equation of motion of a particle executing simple harmonic motion is a+16 π2 x=0 . In this equation, a is the linear acceleration in m s -2 of the particle at a displacement x in metre. The time period in simple harmonic motion is

Question

The equation of motion of a particle executing simple harmonic motion is a+16 π2 x=0 . In this equation, a is the linear acceleration in m s -2 of the particle at a displacement x in metre. The time period in simple harmonic motion is (A) (1/4) s (B) (1/2) s (C) 1 s (D) 2 s

Tardigrade Admin · Accepted Answer

The given equation of SHM is a=-16 π2 x Standard equation of SHM is a=-ω2 x Comparing two equations, we get ω=4 π ∴ T=(2 π/ω)=(2 π/4 π)=(1/2) s

Q. 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 metre. The time period in simple harmonic motion is

$\frac{1}{4} s$

$\frac{1}{2} s$

$1 s$

$2 s$

The given equation of $S H M$ is $a = - 16 π^{2} x$
Standard equation of $S H M$ is $a = - ω^{2} x$
Comparing two equations, we get $ω = 4 π$
$∴ T = \frac{2 π}{ω} = \frac{2 π}{4 π} = \frac{1}{2} s$

Q. The equation of motion of a particle executing simple harmonic motion is a+16π2x=0. In this equation, a is the linear acceleration in ms−2 of the particle at a displacement x in metre. The time period in simple harmonic motion is

41​s

21​s

1s

2s