1. The problem statement, all variables and given/known data A car uniformly accelerates. Show an open door that slams shut will do so in simple harmonic motion. 2. Relevant equations 3. 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 [tex]\theta[/tex] and [tex]\alpha[/tex] that way. Any comments on my ideas or new ideas? Thanks.