Simple Harmonic Motion and a Car

[stanli121]

Homework Statement

A car uniformly accelerates. Show an open door that slams shut will do so in simple harmonic motion.

Homework Equations

The Attempt at a Solution

This seems more conceptual than mathematical. I considered using T = Ia but the problem is the torque would act on the pivot (point where door connects to car) and be R=0 from the axis so T=0. Then I considered F=ma because the acceleration is known to be constant. But I ran into two problems there. First, the displacement I would need to relate to acceleration to show SHM is not clear whatsoever. Second, wouldn't the force about the pivot be centripetal, thus removing my x and d²x/dt²? My newest thought is perhaps choosing a point on the pavement and doing some sort of T = dL/dt type calculation then relating $$\theta$$ and $$\alpha$$ that way. Any comments on my ideas or new ideas?
Thanks.

 

[diazona]

You can calculate the torque around any axis. You're probably used to using pivot points because that's usually the convenient thing to do, but in this case you might want to consider other axes to try.