a particle of mass rest on a smooth plane. the plane is raised to an inclination

Question

a particle of mass rest on a smooth plane. the plane is raised to an inclination angle at a constant rate (=0 at t=0), causing the particle to move down the plane. Determine the motion of the particle by choosing r and as generalized coordinates. You may use any classical mechanics text for studying the motion of driving oscillator. techniques commonly used in solving inhomogeneous second order differential equation encountered in a driven oscillator problem will be useful here. This system is not oscillatory but mathematically similar to driven oscillator problem

thanks

Explanation / Answer

we know that in an incline plane. a=-g*sin(0) where 0 = wt. so that we have. a=-g*sin(wt) so dv/dt=-g*sin(wt) so v=g/w *(cos(wt)-1)=dr/dt at t=0 r=R. so that we have. r=g/w^2 *(sin(wt)-t*w)+R

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