Why Does T^2 Not Directly Correspond to L in Compound Pendulums?

[Mike Shandon]

Hi, I am having some trouble with the following question, any help would be appreciated

1. Homework Statement

For a simple pendulum, T^2 is directly proportional to the length of the string (L)

Why is this not true for a compound pendulum?

Homework Equations

T= 2pi sqrt(l/g) [/B]

The Attempt at a Solution

[/B]
Could it be because the mass of a simple pendulum is concentrated at one point, while the mass of a compound pendulum is spread out

 

[drvrm]

Could it be because the mass of a simple pendulum is concentrated at one point, while the mass of a compound pendulum is spread out

for oscillatory motion the mean position at equilibrium is important-as oscillations results and sustains due to slight diturbance about the equilibrium and the time period is related to the distance between point of suspension and point of oscillation an effective length of the compound pendulum.

 

[haruspex]

Could it be because the mass of a simple pendulum is concentrated at one point, while the mass of a compound pendulum is spread out

Yes. See https://en.m.wikipedia.org/wiki/Pendulum.