A car's 30.0-kg front tire is suspended by a spring with spring constant k=1.00x10^5 N/m. At what speed is the car moving if washboard bumps on the road every 0.750 m drive the tire into a resonant oscillation?

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