Question 366: Oscillations

Question

The quantity which does not vary periodically for a particle performing SHM is

Accepted Answer

For a particle executing simple harmonic motion (SHM),
Total energy $=$ kinetic energy + potential energy
$$\begin{aligned}
& =E_K+E_P=\frac{1}{2} m v^2+\frac{1}{2} k x^2 \
& =\frac{1}{m}\left(A^2-x^2ight)+\frac{1}{2} m \omega^2 A^2 \
& (\because v=\sqrt{A^2-x^2} 	ext { where, } A 	ext { is the } \
& 	ext { amplitude of the particle) } \
& =\frac{1}{2} K A^2
\end{aligned}$$
It is independent of $t, x$ is remains constant i.e., it does not vary periodically.
However, the displacement of a particle executing SHM along $x$-axis is given by
$$x=A \sin (\omega t+\phi)$$
(where, $A=$ amplitude, $\omega=$ angular velocity $t=$ time, $\phi=$ initial phase of the particle)
i.e., displacement varies periodically with time $t$. velocity of particles executing SHM,
$$v=\frac{d x}{d t}=\omega \sqrt{A^2-x^2}$$
which varies with $x$.
Acceleration of the particle,
$$a=\frac{d v}{d t}=-\omega^2 x$$
Which also varies with $x$.

Answer

acceleration

Answer

total energy

Answer

displacement

Answer

velocity

Oscillations

The quantity which does not vary periodically for a particle performing SHM is

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