Pendulum in an accelerating car. Does it oscillate?
If acceleration instantly goes from zero to some constant, the pendulum will oscillate because the net force vector on the bob will suddenly change, just as it does when the bob is held aside and released. The pendulum oscillates around the net force vector, no matter which direction it points to. This might sound wrong because we imagine cars building acceleration slowly, not suddenly as if they were falling sideways. Indeed, acceleration functions exist in which the pendulum moves monotonically. Because pendular oscillation is sinusoidal, and all derivatives of a sinusoid are sinusoidal, it looks like oscillation to anyone with a polynomial position function.
