Question

A particle executes S.H.M from extreme position and covers a distance equal to half of its amplitude in 1 sec. Determine the time period of motion.

Answer 1

Answer:

final answer

Explanation:

$\begin{aligned}&\mathrm{x}=\mathrm{A} \cos \mathrm{wt} \\&\frac{\mathrm{A}}{2}=\mathrm{A} \cos \mathrm{wt} \\&\Rightarrow \mathrm{wt}=\frac{\pi}{3} \\&\Rightarrow \mathrm{t}=\frac{\pi}{3} \mathrm{w} \\&\Rightarrow \mathrm{t}=\frac{\pi}{3} \frac{\mathrm{T}}{2 \pi} \\&\Rightarrow \mathrm{T}=6 \mathrm{t}=6 \mathrm{sec}\end{aligned}$

Therefore the time period of motion is $6$ sec.