If $x=10 \cos \left(2\pi t+\frac{\pi}{6}\right) \mathrm{cm}$ represents the motion of a particle exe

Question

If $x=10 \cos \left(2\pi t+\frac{\pi}{6}\right) \mathrm{cm}$ represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively are

Professor PC Thomas Classes · Answer

(a) : Given equation is $x=10 \cos \left(2\pi t+\frac{\pi}{6}\right) \mathrm{cm}$. Comparing it with the standard SHM equation $x = A \cos(\omega t + \phi)$, we get amplitude $A = 10 \mathrm{~cm}$ and angular frequency $\omega = 2\pi \mathrm{~rad/s}$. The time period is $T = \frac{2\pi}{\omega} = \frac{2\pi}{2\pi} = 1 \mathrm{~s}$.