To explore this issue further, let's look at this simple system - a pendulum. This is a diagram is a little more realistic than the ones usually used in textbooks. In addition to gravity that pulling the bob back to the center, there is friction resisting the movement of the bob, and a driving force adding energy to the system. And I haven't assumed that the angle is so small that the sin of theta equals theta. Note that in addition to the length of the pendulum, the strength of gravity, the amount of friction and the characteristics of the input signal.