Question

Potential energy (sinusoidal curve) is shown graphically for a particle. The potential energy does not depend on Y and z. For range $0<X<2$, maximum value of conservative force is $\beta \pi$(in magnitude). The value of $\beta$ is:(Here this force is corresponding to above-potential energy and all units are in S.I.)

Answer 1

From the graph,

we can conclude that the

$U=3+3\sin Rx$

$k=\frac{2\pi }{\lambda }$

$=\frac{2\pi }{2}=\pi$

$\therefore U=3+3\sin \pi x$

$F=\frac{-\delta U}{\delta x}=\left(9\cos \pi x\right)\times \pi$

$\therefore f$ is max when $\cos \pi x=(-1)$

$\therefore F_{max}=9\pi$