Question

Two particles ‘A’ and ‘B’ perform S.H.M. starting from the mean position, with periodic times T and \[\frac{3T}{2}\], respectively. The phase difference between the particles when particle ‘A’ completes one oscillation will be

Options

• \[\left(\frac{\pi}{4}\right)^c\]

• \[\left(\frac{\pi}{3}\right)^c\]

• \[\left(\frac{\pi}{2}\right)^c\]

• \[\left(\frac{2\pi}{3}\right)^{c}\]

Answer 1

\[\left(\frac{2\pi}{3}\right)^{c}\]

Explanation:

Phase difference,

\[\Delta\phi=\left(\frac{2\pi}{\mathrm{T}_{1}}-\frac{2\pi}{\mathrm{T}_{2}}\right)\mathrm{t}=\left(\frac{2\pi}{\mathrm{T}}-\frac{2\pi}{\frac{3}{2}\mathrm{T}}\right)\mathrm{t}\]

At t = T,

\[\Delta\phi=\left(2\pi-\frac{4\pi}{3}\right)\frac{\mathrm{T}}{\mathrm{T}}=\frac{2\pi}{3}\mathrm{rad}\]