How far apart should speed bumps be placed so that a car will bounce more and more violently? Suppose the suspension system of the average car can be fairly well modeled by an underdamped harmonic oscillator with a natural period of 2 seconds. How far apart should speed bumps be placed so that a car travelling at 15 mph over several bumps will bounce more and more violently with each bump? My idea: An underdamped system would have the damping coefficient $\gamma <2 \sqrt{km}$, where $k$ is the spring coefficient and $m$ is the mass of the car. Neither of these values were provided in the problem. Since the car is travelling at 15 mph, $u'(t)=15$mph. The period is 2 seconds, so $2=T=2\pi / \omega_0$, which implies $\omega_0=\pi$. This is the most amount of information that I could extract from this problem. How should I approach solving this problem?

I am assuming this problem is from a physics/engineering class and to solve it you are supposed to use the fact that you achieve an increasing amplitude if you push the harmonic oscillator at it's eigenfrequency. Thus, the bumps should happen every two seconds. So you just need to calculate how far a car with 15 mph travels in 2 seconds.

If this answer does not satisfy you, let me know so I can provide you one including the ODE.