If a simple harmonic motion is represented by $\frac{d^{2}x}{dt^{2}}+\alpha x=0$, its time period is

(B) $\frac{2\pi}{\sqrt{\alpha}}$

JEE Main · 2005 · 08 May 2005 · Offline · Elasticity & SHM

If a simple harmonic motion is represented by

\frac{d ^{2} x}{d t ^{2}} + α x = 0

, its time period is

Answer: (B)

Comparing

\frac{d ^{2} x}{d t ^{2}} + α x = 0

with the standard form

\frac{d ^{2} x}{d t ^{2}} + ω^{2} x = 0

identifies

ω^{2} = α

, so

ω = α

and the period is

T = \frac{2 π}{ω} = \frac{2 π}{α}

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option