Hello people I have a problem with this exercise.
I need to show that a motion of a pendulum can be found by solving the differential equation
with x=0 at t=0
The problem arises when I try to rearrange the equation and calculate the integral of which brings me nowhere. Anyone has any idea on how to solve this differential equation?
Also, I can't do the next part of the question, which is using Eulers method with t=0.1 to estimate x(0.3) if I don't find first a solution to the equation.
Any help would be greatly appreciated
As for using Eulers Method .... you don't need to have solved the differential equation in order to apply this method! It is a method for getting a numerical approximation to a solution.
the question is about a spherical pendulum which has an equation of . It then tells you to assume that the pendulum is set in motion from the vertical with angular velocity 1 so that x=0 and dx/dt=1 at t=0. It then asks to show that the subsequent motion can be found by solving the differential eqn i posted earlier.
And I just used x instead of angle theta so x should be an angular quantity