Question

The maximum force acting on a particle executing simple harmonic motion is $10\, N$. The force on the particle when it is midway between mean and extreme positions will be

• A. 10 N
• B. 12 N
• C. 5 N
• D. 0

Answer 1

Answer: (C)

Maximum force on the particle performing $S H M, F_{\max }=10\, N$
We know that, In SHM, when body is at maximum displacement (amplitude $a$ ), then force on the particle is maximum.
$\therefore F_{\max }=$ mass $\times$ acceleration $=m \cdot \alpha_{\max }$
$\left[\therefore \alpha_{\max }=\omega^{2} a\right]$
$\Rightarrow 10=m \cdot \omega^{2} a$
$\Rightarrow 10=m a \omega^{2} \ldots$ (i)
Force on the particle when it is mid way $\left(y=\frac{a}{2}\right)$ between mean and extreme position,
$F=m \omega^{2} y=m \omega^{2} \cdot\left(\frac{a}{2}\right)$
$\left[\because y=\frac{a}{2}\right]$
$=\frac{m a \omega^{2}}{2}=\frac{10}{2}$ [from Eq (i)]
$=5\, N$