Question

The time period of a particle in SHM does not depend upon its:

• A. Frequency
• B. Acceleration
• C. Amplitude
• D. It depends on all the above.

Answer 1

Answer: (B)

$x=Asin(\omega t+\theta )$
$\frac{d^{2}x}{d{t}^2}=a=-{\omega }^{2}x$
According to Hooke's Law
$F=-kx$
$ma=-kx$
$m(-{\omega }^{2}x)=-kx$
$\omega =\sqrt{\frac{k}{m}}$
Now, $\omega =\frac{2\pi }{T}$
where T is time periond. Therefore,
$T=2\pi \sqrt{\frac{m}{k}}$. It does not depend on acceleration and amplitude. It does depends on frequency as $T=\frac{1}{f}$ where $f$ is frequency.