If $x=5 \sin \left(\pi t+\frac{\pi}{3}\right) \mathrm{m}$ represents the motion of a particle execut

Question

If $x=5 \sin \left(\pi t+\frac{\pi}{3}\right) \mathrm{m}$ represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively are

Professor PC Thomas Classes · Answer

(b) : Given : $x=5 \sin \left(\pi t+\frac{\pi}{3}ight) \mathrm{m}$ Comparing the given equation with the standard equation of simple harmonic motion \ $ x=A \sin (\omega t+\phi) $ we get, $A=5 \mathrm{~m}$ and \ $\omega=\pi$ Time period, $T=\frac{2 \pi}{\omega}=\frac{2 \pi}{\pi}=2 \mathrm{~s}$