Why does length affect the time for an oscillation in a simple pendulum?
The acceleration (not the angular acceleration!) of the pendulum towards the center does not depend on the displacement from the center, but on the angle that it makes. And the angle is approximately the displacement divided by the length of the pendulum. That is where the length comes in. [Edit] Yes, the oscillation period does only depend on the length of the rope and not on the amplitude. At least, for small amplitudes. The driving force behind the oscillation is gravity. When you move the mass point to the side, it also gets lifted. When the rope is longer, the mass point gets lifted less when you dispace it by the same amount, so the gravitaional force involved is smaller. When you give a longer rope the same angular displacement, the force will be the same compared to a shorter rope, but the mass point has to cover a larger distance during an oscillation. These two effects both cause the oscillation period to be longer for a longer rope.
