we know the equation for the period of oscillation in SHM is as follows:
T = 2 * pi * sqrt(mass/k)
we know f = 1/T, so f = 1/(2 * pi) * sqrt(k/m).
since d = v*T, we can say v = d/t = d * f
the final equation, after combining everything, is as follows:
v = d/(2 * pi) * sqrt(k/m)
by plugging everything in
v = .75/(2 * pi) * sqrt((1 * 10^5)/(30))
We find our velocity to be:
v = 6.89 m/s
