Science-Relationship between length of string holding a weight in relation to the time it takes to swing?

C

Cameron

New member
So I have an assignment in Science. We've had a few periods to design an experiment to see:
"If the length of a simple pendulum (string holding a 50g weight) affects the time the pendulum takes to complete 5 swings (there and back).

So I was just wondering if anybody knows if there is any scientific reasoning to suggest why shorter string is faster to swing than longer string etc. I want to know if there is any specific Physics-Based Theory behind it that may involve a calculation.

Your thoughts would really help as it is due tomorrow :/
 
Think of it this way. If you had two pendulums (pendula ?) which were identical except that one was longer than the other, and that they were both pulled aside say 10 degrees. The forces would be the same on both. So when released they would initially both accelerate toward equilibrium at the same rate. But for the shorter pendulum the distance to the equilibrium point is less so less time would be required to get there. As a result the short pendulum would complete a cycle in less time than the longer one.
[by "equilibrium point" I mean the point at which the pendulum hangs vertically]
 
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