- #1
leonmate
- 84
- 1
Homework Statement
I've attached an image of the problem question, it's Q1 I'm working on
This is what I have so far:
we have two components of SHM, position x and velocity v.
when x = 0, v = a maximum, when v = 0, x = a maximum
this is represented by sin & cos functions.
where x = A*sin(w*t*phi)
and v = A*w*cos(w*t*phi)Here it can be shown that a = -w^2 * x
thus, dv/dt = -w^2 * x
and, dv/dt = dv/dx * dx/dt = -w^2 * x
and, v*dv/dx = -w^2 * x
then we're left with differential equation, v*dv = -w^2 *x*dxSo the last equation: v dv = -ω2x dx
Would this be considered two linear ordinary equations?? I'm a little unsure about the question is actually asking me - 'the analytical solution'
I've got to code this with python, and solve using euler and fourth-order Runge-Kutta method - I've already made solver functions to do both these things, I just can't progress past q1! ..frustratingAny help would be very appriciated
Leon