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

• Mike Shandon
In summary, the statement that T^2 is directly proportional to the length of the string (L) is not true for a compound pendulum due to the mass being spread out and the importance of the mean position at equilibrium for oscillatory motion.
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

Mike Shandon said:
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.

Mike Shandon said:
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.

## 1. What is a simple pendulum?

A simple pendulum is a weight suspended from a fixed point that is able to swing back and forth. It consists of a mass called the bob and a string or rod attached to a fixed point at the other end. The motion of a simple pendulum is governed by gravity and the length of the string.

## 2. What is a compound pendulum?

A compound pendulum is a pendulum with a rigid body instead of a single mass at the end. The rigid body can have varying shapes, such as a rod or a physical object. The motion of a compound pendulum is governed by gravity, the length of the string, and the distribution of mass within the rigid body.

## 3. What factors affect the period of a simple or compound pendulum?

The period of a pendulum is affected by its length, the acceleration due to gravity, and the amplitude of the swing. For a simple pendulum, the period is also affected by the mass of the bob. For a compound pendulum, the period is also affected by the distribution of mass within the rigid body.

## 4. What is the formula for calculating the period of a pendulum?

The formula for calculating the period of a pendulum is T = 2π * √(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. This formula applies to both simple and compound pendulums, as long as the length is measured from the point of suspension to the center of mass of the pendulum.

## 5. How does the angle of release affect the period of a pendulum?

The angle of release, also known as the amplitude, does not significantly affect the period of a pendulum as long as it is small (less than 15 degrees). The period of a pendulum is only affected by the length and acceleration due to gravity. However, larger amplitudes can result in a longer period due to the pendulum's motion becoming more complex and less regular.

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