The displacement of simple harmonic oscillator after \(3\) seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is \(\dots \; s\)

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Answer & Solution

Correct Answer

(D) \(36\)

Detailed explanation

\(X=A \sin \omega t\left(t=3, X=\frac{A}{2}\right)\)

\(\Rightarrow \frac{A}{2}=A \sin 3 \omega\)

\(\Rightarrow \sin 3 \omega=\frac{1}{2}\)

\(\Rightarrow 3 \omega=\frac{\pi}{6}\)

\(\Rightarrow \omega=\frac{\pi}{18}=\frac{2 \pi}{T}\)

\(\Rightarrow T=36 \; s\)

Same subject

List \(I\)	List \(II\)
\((A)\) Young's Modulus \((Y)\)	\((I)\) \(\left[ M L ^{-1} T ^{-1}\right]\)
\((B)\) Co-efficient of Viscosity \((\eta)\)	\((II)\) \(\left[ M L ^2 T ^{-1}\right]\)
\((C)\) Planck's Constant \((h)\)	\((III)\) \(\left[ M L ^{-1} T ^{-2}\right]\)
\((D)\) Work Function \((\phi)\)	\((IV)\) \(\left[ M L ^2 T ^{-2}\right]\)

From JEE Mains