Question

a particle of mass m moves on a horizontal smooth line AB of length a such that when particle is at any general pt Pie on d line two forces act on it. a force mg(AP)/a towards A and another force 2mg(BP)/a towards B.
(1). show that particle perform SHM on line when release from rest from mid pt of line AB.
(2). find time period and amplitude.
(3). find minimum distance of particle from B during the motion.
(4). force acts towards A stops acting when the particle is nearest to B then find velocity with which it crosses pt B



please answer this question ASAP

Answer 1

dW = Fdx

dW = Madx  

dW =  Mvdv/dx  * dx

 dW = M * a√x * a/2√x dx

dW = M * a^2/2 dx

Integerating both sides with limits x =0 to x = d we get,

W = (Ma^2/2)d – 0

    = (Ma^2/2)d Joule.