Question

A particle is executing a simple harmonic motion. Its maximum acceleration is $\alpha$ and maximum velocity is $\beta$ Then, its time period of vibration will be

• A. $\frac{{\beta }^2}{\alpha }$
• B. $\frac{2\pi \beta }{\alpha }$
• C. $\frac{{\beta }^2}{{\alpha }^2}$
• D. $\frac{\alpha }{\beta }$

Answer 1

Answer: (B)

lf A and $\omega$ be amplitude and angular frequency of vibration, then
$\alpha ={\omega }^{2}A$ ...(i)
and $\beta =\omega A$ ...(ii)
Dividing eqn. (i) by eqn. (ii), we get
$\frac{\alpha }{\beta }=\frac{{\omega }^{2}A}{\omega A}=\omega$
$\therefore$ Time period of vibration is
T = $\frac{2\pi }{\omega }=\frac{2\pi }{(\alpha /\beta )}=\frac{2\pi \beta }{\alpha }$