Acar’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

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