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In SHM restoring force is $F=-k x$, where $k$ is force constant, $x$ is displacement and $A$ is amplitude of motion, then total energy depends upon
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Verified Answer
The correct answer is:
$k, A$
In SHM, the total energy
Or
$$
\begin{array}{l}
=\text { potential energy }+\text { kinetic energy } \\
E=U+K
\end{array}
$$
$$
\begin{aligned}
=& \frac{1}{2} m \omega^{2} x^{2}+\frac{1}{2} m \omega^{2}\left(A^{2}-x^{2}\right) \\
&=\frac{1}{2} m \omega^{2} A^{2}=\frac{1}{2} k A^{2} \\
\text { where } k=\text { force constant }=m \omega^{2}
\end{aligned}
$$
Thus, total energy depends on $k$ and $A$.
Or
$$
\begin{array}{l}
=\text { potential energy }+\text { kinetic energy } \\
E=U+K
\end{array}
$$
$$
\begin{aligned}
=& \frac{1}{2} m \omega^{2} x^{2}+\frac{1}{2} m \omega^{2}\left(A^{2}-x^{2}\right) \\
&=\frac{1}{2} m \omega^{2} A^{2}=\frac{1}{2} k A^{2} \\
\text { where } k=\text { force constant }=m \omega^{2}
\end{aligned}
$$
Thus, total energy depends on $k$ and $A$.
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