# As time period doesnot depend on amplitude so then why it is said that in measurement of time period amplitude must be kept small and also that amplitude must be zero ?

##### 2 Answers

Because large amplitudes (beyond

#### Explanation:

If you look at the derivation it includes the line that the restoring force is proportional to

This is less true as

The Explanation describes why that is true for a simple pendulum.

#### Explanation:

You did not say what was oscillating. I will answer for the case where it is a simple pendulum that is oscillating. If it is a pendulum, amplitude must be small because the "time period does not depend on amplitude" rule applies to pendulums *only* if it is exhibiting simple harmonic motion.

Simple harmonic motion of a physical system requires that the force restoring the object (bob) to the equilibrium position must be proportional to the displacement from the equilibrium position.

Go to the site

http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html

Scroll down to the section with a heading of "Period of Simple Pendulum". The first formula in that section is

The angle theta (in radians) is the displacement. This equation comes from valid application of trigonometry.

In that formula, m and g are constants. Therefore this formula says that

are proportional. But the rule for simple harmonic motion says that

must be proportional. You know that sine is not a linear relation to the angle. It plots a sine wave. But, when the value of

When this approximation is valid that initial formula can be written

So in that form, we see that

So, when amplitude is kept small (allowing use of the

I hope this helps,

Steve

P.S. I do not know why you may have seen "also that amplitude must be zero".