Q. A particle of mass $m$ is under the influence of a force $F$ which varies with the displacement $x$ according to the relation $F = - kx + F_{0}$ in which $k$ and $F_{0}$ are constants. The particle when disturbed will oscillate
A) About $x = 0$, with $\omega \neq \sqrt{k/m}$
B) About $x = 0$, with $\omega = \sqrt{k/m}$
C) About $x = F_{0}/k$, with $\omega = \sqrt{k/m}$
D) About $x = F_{0}/k$, with $\omega \neq \sqrt{k/m}$
Explanation
(c) Restoring force is zero at mean position
$F = - Kx + F_{0} \Rightarrow 0 = - Kx + F_{0} \Rightarrow x = \frac{F_{0}}{K}$
$i.e.$ the particle will oscillate about $x = \frac{F_{0}}{K}$
$\Rightarrow F_{0} = Kx \Rightarrow ma = Kx \Rightarrow a = \frac{K}{m}n\therefore W = \sqrt{\frac{K}{m}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.