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

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.