Why does the angle of release not affect the time for one swing of a pendulum?Please help me - coursework!!!?

Question

I need to know why the angle of release does not affect the time for one oscillation of a pendulum. This is for my GCSE Pendulum Coursework Please serious aand detailed answers only - best one gets 10pts! Thanks very much!

Answer 1

1. See, Galileo discovered that the pendulum with a certain length will have only a certain time period even if you release it at an angle of 89 degrees. Because, if you release it from a greater height, i.e. at a greater angle, it will come down and go up with greater speed. So, the time will be same as the distance also increases. But if you release it from a lesser height, i.e. at a lesser angle, it will come down and go up with lesser speed. So, the time will be same as the distance also decreases.

2. As already pointed out, at small angles the sine of the angle is approximately equal to the angle (in radians). This means that if you double the angle of release you will double the force towards the centre and hence the acceleration (a condition for simple harmonic motion). You can see that the extra distance travelled (twice as much) is exactly offset by the increase in speed which means the period will be independent of the angle.

3. the time of penduilum oscillation is proportional to the squareroot of its length and independent of angle of release

4. When you pull your pendulum to a higher position it will have a velocity, at the bottom of the swing that is larger than if you started at a lower position. So there will be some kind of ratio where ...you have a larger distance to cover (higher starting position) with a large velocity, but on the same note you have a small distance to cover (lower position) with a small velocity. The ration will balance in a way that causes the period to remain pretty much unchanged.