Newtonian Mechanics – Why Does a Pendulum Swing the Way It Does?

Question

this might be a silly question so feel free to tell me to change it / clarify if it's too vague to answer. But why is is that a pendulum swings the way it does? I'm not talking about its period, or the duration of the swing or the peak points it reaches, but rather the underlying movement for all these attributes. When held at its "peak", so either the left or right corner, it's being affected I imagine by a couple things, one being the forces interacting between the rope and the ball,and the hand or object holding it at rest and the other being gravity. I imagine the instant you let it go, it's being largely affected by gravity, but after that instant, it begins to gain velocity in the horizontal plane. Where does this horizontal velocity come from? The best I could do was take a spanner wrench (which is L shaped) and try to simulate what happens with my thumb acting as the hand holding the object at rest. One thing I noticed was if I hold the spanner horizontally, and push up on the anchor part (the part which would act as a pendulums anchor) while pushing down on its base, it looks like the same motion as the pendulum. So is that an explanation of sorts? that the anchor is being pushed up? Again sorry if this is too much of a word vomit, If there's anything you need me to clarify don't hesitate.

Answer 1

I imagine the instant you let it go, it's being largely affected by gravity, but after that instant, it begins to gain velocity in the horizontal plane. Where does this horizontal velocity come from?

After it is released there are two forces acting on the pendulum - these are its weight, and the tension in the string. Its weight acts vertically, and so has no horizontal component. However, the tension in the string is at a (small) angle to the vertical so it does have a horizontal component. There is no other horizontal force on the pendulum to counteract this, so the horizontal component of the tension in the string accelerates the pendulum and gives it a horizontal velocity back towards its equilibrium point (the lowest point of its swing). Once it passes its equilibrium point, the horizontal component of the tension in the string now acts in the opposite direction and reduces the horizontal velocity of the pendulum until it reaches the opposite extreme of its swing, when it is momentarily stationary. Then, in the second half of its swing, everything repeats but in reverse.