MHT CET · Physics · Mechanical Properties of Solids
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
- A \(k, A\) and \(M\)
- B \(k, x, M\)
- C \(k, A\)
- D \(k, x\)
Answer & Solution
Correct Answer
(C) \(k, A\)
Step-by-step Solution
Detailed explanation
In SHM, the total energy
Or
\(\begin{array}{l}=\text { potential energy }+\text { kinetic energy } \\E=U+K\end{array}\)
\(=\frac{1}{2} m \omega^{2} x^{2}+\frac{1}{2} m \omega^{2}\left(A^{2}-x^{2}\right) \)
\(=\frac{1}{2} m \omega^{2} A^{2}=\frac{1}{2} k A^{2} \)
\(\text { where } k=\text { force constant }=m \omega^{2}\)
Thus, total energy depends on \(k\) and \(A\).
Or
\(\begin{array}{l}=\text { potential energy }+\text { kinetic energy } \\E=U+K\end{array}\)
\(=\frac{1}{2} m \omega^{2} x^{2}+\frac{1}{2} m \omega^{2}\left(A^{2}-x^{2}\right) \)
\(=\frac{1}{2} m \omega^{2} A^{2}=\frac{1}{2} k A^{2} \)
\(\text { where } k=\text { force constant }=m \omega^{2}\)
Thus, total energy depends on \(k\) and \(A\).
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