Question

The maximum velocity of a harmonic oscillator is d and its maximum acceleration is $\beta$. Its time period will be

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

Answer 1

The correct option is C

$\frac{2\pi d}{\beta }$

$V_{max}=x_0\omega a_{max}=x_0{\omega }^2$

$\therefore \omega =\frac{a_{max}}{v_{max}}=\frac{\beta }{d}$

or $\omega =\frac{2\pi }{T}=\frac{\beta }{d}orT=\frac{2\pi d}{\beta }$