A block of mass m is attached to a spring of spring constant k is free to oscillate with angular velocity `omega` in a horizontal plane without friction or clamping. It is pulled to a distance `x_(0)` and pushed towards the centre with a velocity `v_(0)` at time t=0. the ammplitude of oscillationsin terms of `omega,x_(0) and v_(0)` is

Explanation

x= A `cos (omega x + theta) `, velocity , `(dx)/(dt) =- A omega sin(omegat + theta)`
When t=0 , `x=x_0 and (dx)/(dt) = -v_0`
`therefore x_0 = A cos theta " "……..(i)`
`-v_0 = - A omega theta ` (or) ` A sin theta = v_0//omega " "......(ii)`
Squaring and adding (i) and (ii) , we get , `A^2 (sin^2 theta + cos^2 theta) = (v_0^2 //omega^2) + x_0^2 , A= [v_0^2 .//omega^2 + x_0^2J^(1//2)]`