Question

The maximum force acting on a particle executing simple harmonic motion is $10N$. 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 $SHM,F_{\max }=10N$
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 $=m\cdot {\alpha }_{\max }$
$\left[\therefore {\alpha }_{\max }={\omega }^{2}a\right]$
$\Rightarrow 10=m\cdot {\omega }^{2}a$
$\Rightarrow 10=ma{\omega }^2\dots$ (i)
Force on the particle when it is mid way $\left(y=\frac{a}{2}\right)$ between mean and extreme position,
$F=m{\omega }^{2}y=m{\omega }^2\cdot \left(\frac{a}{2}\right)$
$\left[\because y=\frac{a}{2}\right]$
$=\frac{ma{\omega }^2}{2}=\frac{10}{2}$ [from Eq (i)]
$=5N$