The velocity of a slider is defined by the relation v = v sin (nt + ).

The velocity of a slider is defined by the relation v = v ‘sin (ωnt + ϕ). Denoting the velocity and the position of the slider at t = 0 by v0 and x0, respectively, and knowing that the maximum displacement of the slider is 2x0, show that
(a) v'= (v20 + x20 ω2n) /2x0ωn,
(b) The maximum value of the velocity occurs when x = x0 [3 − (v0/x0wn)2]//2.