Question

1. A particle of mass m is repelled from the origin by a force f= k/x3, where x is the distance from the origin. Solve the equation of motion, if the particle is initially at rest at a distance x0 from the origin. 

Answer 1

Answer

Using newton law

$f=ma=m\frac{d^2x}{dt^2}=k/x^3$

Particle goes 0 to x₀ in time 0 to the

Solving above equation

$\frac{dx}{dt}=-k/2mx^2+c$

At t=0 V=0 so C=0

Again integrate

$\frac{dx}{dt}=-k/2mx^2$

$\int_0^{x_0}2x^2 dx=-\int _0^tkdt/m$

$\frac{2x_0^3}{3}=-kt/m$