# Simple Pendulum and speed

1. Dec 5, 2014

### zippeh

1. The problem statement, all variables and given/known data
You pull a simple pendulum of length 0.260m to the side through an angle of 3.50∘ and release it.

Part A:
How much time does it take the pendulum bob to reach its highest speed?

Part B:
How much time does it take if the pendulum is released at an angle of 1.75∘ instead of 3.50∘?

2. Relevant equations
T=2π√(m/k)

3. The attempt at a solution

I got the correct answer of t = 0.256s, but I do not understand why it doesn't change according to the change in the angle. Our masterphysics homework site has a online app that allows us to work with a simple pendulum. When I change the angle (lets say from 1° to 90°), I get different values that it takes to reach the very bottom (0°). This position in the pendulum will be the position of greatest velocity because there is no potential energy. Can someone explain what I am missing here? Thank you so much.

2. Dec 5, 2014

### Orodruin

Staff Emeritus
When the angle is just 3.5 degrees, you can make a small-angle approximation which works pretty well. It is only in this approximation the pendulum will perform harmonic oscillation and thus have a fixed period. A right angle is by no means small and you therefore cannot make the small angle approximation for that case (or for any large initial angles).