Physics | VITEEE 2019 | Discussion Page

If the differential equation for a simple harmonic motion is $\frac{d^{2}y}{dt^{2}}+2y = 0$, the time period of the motion is

A) $\pi\sqrt{2}$ sec

B) $\frac{\sqrt{2s}}{\pi}$ sec

C) $\frac{\pi}{\sqrt{2}}$ sec

D) $2\pi$ sec

Option A

The differential equation of simple harmonic motion is

$\frac{d^{2}y}{dt^{2}}+2y = 0$ or $\frac{d^{2}y}{dt^{2}} = -2y$ ...(i)

Standard equation of simple harmonic motion is

$\frac{d^{2}y}{dt^{2}}$ =- ω² y ....(ii)

Comparing eq. (i) and (ii)

ω² = 2 or ω = √2

As we know,

$\omega = \frac{2\pi}{T}$

.'. TimePeriod, T = $\frac{2\pi}{\omega}$

= $\frac{2\pi}{\sqrt{2}}$ = $\pi\sqrt{2}$ sec

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