The equation of motion of a simple harmonic oscillator is d2ydt2+104π2y=0 The time period of the oscillator is

d2ydt2+104π2y=0d2ydt2+ω2y=0ω2=104π2⇒ω=102π⇒2πT=102π⇒T=2100=0.02 s

The equation of motion of a simple harmonic oscillator is d2ydt2+104π2y=0 The time period of the oscillator is

d2ydt2+104π2y=0d2ydt2+ω2y=0ω2=104π2⇒ω=102π⇒2πT=102π⇒T=2100=0.02 s

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The equation of motion of a simple harmonic oscillator is $\frac{d^{2} y}{d t^{2}} + 10^{4} π^{2} y = 0$ The time period of the oscillator is

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50 s

5 s

0.2 s

0.02 s

answer is D.

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Detailed Solution

$\frac{d^{2} y}{d t^{2}} + 10^{4} π^{2} y = 0$
$\begin{array}{l} \frac{d^{2} y}{d t^{2}} + ω^{2} y = 0 \\ ω^{2} = 10^{4} π^{2} \Rightarrow ω = 10^{2} π \Rightarrow \frac{2 π}{T} = 10^{2} π \\ \Rightarrow T = \frac{2}{100} = 0.02 s \end{array}$