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

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
  1. $5 \mathrm{~m}, 2 \mathrm{~s}$
  2. $5 \mathrm{~cm}, 1 \mathrm{~s}$
  3. $5 \mathrm{~m}, 1 \mathrm{~s}$
  4. $5 \mathrm{~cm}, 2 \mathrm{~s}$

Solution

$\begin{aligned} & \therefore x=5 \sin \left(\pi t+\frac{\pi}{3}\right) \mathrm{m} \\ & \text { Amplitude }=5 \mathrm{~m} \\ & \omega=\pi=\frac{2 \pi}{T} \\ & T=\frac{2 \pi}{\pi}=2 \mathrm{~s}\end{aligned}$ .

Asked in: NEET 2024

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