First slide

Simple harmonic motion

Question

The equation of motion of a particle is $\frac{d^{2} y}{{dt}^{2}} + Ky = 0$ , where K is positive constant. The time period of the motion is given by

Moderate

A

$\frac{2 π}{K}$
B

$2 πK$
C

$\frac{2 π}{\sqrt{K}}$
D

$2 π \sqrt{K}$

Solution

On comparing with standard equation $\frac{d^{2} y}{{dt}^{2}} + ω^{2} y = 0$ we get $ω^{2} = K \Rightarrow ω = \frac{2 π}{T} = \sqrt{K} \Rightarrow T = \frac{2 π}{\sqrt{K}}$ .

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