Mechanics help,find the particular solution and amplitude

[smithy100]

a block P of mass m lies on a smooth plane AB that is inclined at angle (alpha) to the horizontal.The block is attatched to the bottom of the plane,A, by a spring of stiffness 2k and natural length L0.The block is initially released from rest from the equilibrium position.the equilibrium position of the block ,measured from A along the slope is L0-(mg/2k)sin(alpha)
a)find the particular solution of the differential equation that satisfies these initial conditions
b)write down the period and amplitude of the subsequent motion

can some one show me how this is done thanks
how do i find the amplitude?

 

[member 553083]

a) The particular solution of the differential equation that satisfies these initial conditions is given by:y(t) = L0 - (mg/2k)sin(α) + Acos(ωt)where A is the amplitude, and ω is the angular frequency of the motion. The angular frequency is given by:ω = √(2k/m)b) The period of the motion is T = 2π/ω, and the amplitude is given by A.