calculate the period of a pendulum if the length of the pendulum is o.8m. what is the period if the angular deflection is 30 degrees? 45 degrees?
Although the period does depend slightly upon the angular deflection in the exact solution, the formula that is usually used for the period is
P = (2 pi)*sqrt (L/g)
If L = 0.8 m, you will get a period of
1.795 seconds using that formula, withy g = 9.8 m/s^2.
Using the exact formula, the period is longer by a factor
1 + {(1/2) sin(A/2)]^2 + [(3/8)sin^2(A/2)]^2+ ...}
= (1 + 0.0366 + 0.0030 + ..}
= 1.0396 at A = 45 degrees
So the true period for that angle is
1.866 seconds
Go ahead and do the 30 degree case with the same formu;a, if you must.
The exact formula can be found in F.R.E Crossley's "Dynamics in Machines", published by Ronald Press, 1954. It can probably also be found online.