Thread: irritating differential equation

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

Originally Posted by dumbguy321

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

Some clarifications have been established in this thread: http://www.mathhelpforum.com/math-he...-equation.html

I don't have time to say more at the moment.

sorry for posting twice. This question is for my homework tmoro, I'd posted it in the differential equations file and I thought I wouldnt get fast enough reply.
Anyway im sorry, thanks for ur time, I'v figured how to do the question now.