Why doesnt the angle that a pendulum is released not affect the time it takes to complete one swing...?

Question

the angle - the amplitude etc...

Why does it NOT effect the time

thank s

Answer 1

Well actually it does if the angle is large.

If the angle is small enough that you can approximate the tangential force of gravity, g sin(theta) as g theta, then the equation of motion is linear (theta'' = -g/l theta), and its solution is simple harmonic motion, whose period, 2pi sqrt (l/g), is not dependent on amplitude.

But for a larger angle, all bets are off:

The first few terms of the period as a function of angle are:

T = sqrt (l/g)*(1 + 1/4 sin^2(theta/2) + 9/64 sin^4 (theta/2) +....)

http://en.wikipedia.org/wiki/Pendulum#Si...

Answer 2

Because gravity affects the same in all directions