hey guys, im having extreme difficulties with this question, mostly trying to figure out exactly what the question is asking, if you could give any help it would be appreciated.
The differential equation governing the angle theta
subtended by a spherical pendulum with
the downward vertical is:
d^2theta/dt^2 - x = 2cost
(a) The period of a spherical pendulum is given by the complete elliptic integral of the first kind K, which is
K(m) = integral of dtheta/sqrt(1-m*sintheta^2) in the intervals of pi/2 and 0
Take m = 0:5 and use the Trapezoidal rule with step sizes pi/8 and pi/16 to estimate
K
(0.5). Then use Richardson extrapolation to obtain an improved estimate for
K
(0.5).
(b) Assume that the pendulum has been set in motion from the vertical with angular
velocity 1, so that theta= 0 and dtheta/dt = 1 at t = 0. Show that the subsequent motion of the pendulum can be found by solving the differential equation
dtheta/dt = sqrt(2costheta-1)
with theta = 0 at t = 0 use euler's method with step size delta(t) = 0.1 to estimate 0.3
dtod with step size t = 0:1 to estimate (0:3).
If any1 could also tell me how to write out these equations properly, tht would be very handy indeed
Many thanks,
dumbguy321