Question
Explain the total energy in simple harmonic motion and show the graphical representation of energy in SHM.
✓
Answer
The total energy of the system of a block and a spring is equal to the sum of the potential energy stored in the spring plus the kinetic energy of the block and is proportional to the square of the amplitude.
$
\begin{aligned}
& \frac{1}{2} m \omega^2\left(A^2-x^2\right)+\frac{1}{2} m \omega^2 x^2 \\
& E=\frac{1}{2} m \omega^2 A^2
\end{aligned}
$
Hence, the total energy of the particle in SHM is constant and it is independent of the instantaneous displacement. Relationship between potential energy, kinetic energy, and time in Simple Harmonic Motion at $t=0$, when $x= \pm A$.
$
\begin{aligned}
& \frac{1}{2} m \omega^2\left(A^2-x^2\right)+\frac{1}{2} m \omega^2 x^2 \\
& E=\frac{1}{2} m \omega^2 A^2
\end{aligned}
$
Hence, the total energy of the particle in SHM is constant and it is independent of the instantaneous displacement. Relationship between potential energy, kinetic energy, and time in Simple Harmonic Motion at $t=0$, when $x= \pm A$.
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