Pendulum Concept

[greenseeking]

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Hi,

On TBR's CBT test 4 it says, that the pedulum's frequency/period stays the same even though it loses energy. How does this work?

Total E= PE + KE +( friction)
PE=mgL(1-costheta)
KE=1/2mv^2

so as friction or air resistance decreases the total energy, you should travel less distance and also with less speed. But KE is porportional to v^2 whereas PE is proportional to the distance. So shouldn't the v (velocity) be changing MORE, thereby frequency should be increasing?

 

[BB8730]

A pendulum is a cyclical process that follows f=1/T, which does not change if the amplitude decreases.

Think of it like a piano string - when you hit a note on a piano, the string always vibrates at the same frequency no matter how hard or soft you hit it. The string also continues to vibrate at the same frequency as the sound diminishes. The same goes for a pendulum losing energy.