Question

A particle of mass $10g$ is executing simple harmonic motion with an amplitude of $0.5m$ and periodic time of $\left(\frac{\pi }{5}\right)s$. The maximum value of the force acting on the particle is:

• A. $25N$
• B. $5N$
• C. $2.5N$
• D. $0.5N$

Answer 1

Answer: (D)

$0.5N$

Given : $A=0.5$ $m$ $T=\frac{\pi }{5}$ $s$

Mass of particle $m=10$ $g$ $=0.01$ $kg$

$\therefore$ Maximum acceleration $a={\omega }^{2}A$

$⟹$ $a=(\frac{2\pi }{T}{)}^{2}A$

$\therefore$ $a=(\frac{2\pi }{\frac{\pi }{5}}{)}^2\times 0.5=50$ $m{s}^{-2}$

Maximum force $F=ma=0.01\times 50=0.5$ $N$