In S.H.M. the displacement of a particle at an instant is $\mathrm{Y}=\mathrm{A} \cos 30^{\circ}$, where $\mathrm{A}=40 \mathrm{~cm}$ and kinetic energy is 200 J . If force constant is $1 imes 10^{\mathrm{x}} \mathrm{N} / \mathrm{m}$, then x will be $\left(\cos 30^{\circ}=\sqrt{3} / 2 ight)$

Question

In S.H.M. the displacement of a particle at an instant is $\mathrm{Y}=\mathrm{A} \cos 30^{\circ}$, where $\mathrm{A}=40 \mathrm{~cm}$ and kinetic energy is 200 J . If force constant is $1 	imes 10^{\mathrm{x}} \mathrm{N} / \mathrm{m}$, then x will be $\left(\cos 30^{\circ}=\sqrt{3} / 2ight)$

Aicharya · Accepted Answer

$\begin{aligned} & Y=A \cos 30^{\circ}=40 	imes \frac{\sqrt{3}}{2}=20 \sqrt{3} \mathrm{~cm} \ & 	ext { K.E. }=\frac{1}{2} k\left(A^2-Y^2ight) \ & 200=\frac{1}{2} k\left(\frac{1600}{10^4}-\frac{1200}{10^4}ight)\end{aligned}$ $\begin{aligned} & 200=\frac{1}{2} k\left(\frac{400}{10^4}ight) \ & k=10000=1 	imes 10^4 \ 	herefore \quad & x=4\end{aligned}$

In S.H.M. the displacement of a particle at an instant is $\mathrm{Y}=\mathrm{A} \cos 30^{\circ}$, where…

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