Rotating Spring-Mass system ODE45 function

I need to plot the motion of a mass sliding in a slot in a circular disk(gravity into page) while connecting to a spring centered at the center of the disk. The plot is supposed to show x vs y rather than the x or y components vs time. Does anyone know the proper x and y equations of motion that would apply here?

[Jan]

The description as text is not clear enough. Did you made a drawing already?

Creating the equations on motion is not a Matlab problem, so it is off-topic in this forum.

Do you want to solve this by a DAE with depending coordinates or an ODE with independent coordinates?

Answer 1

[William Rose]

Find x(t) and y(t) then plot x vs y.

You did not mention friction so we assume there is none. So the equations of motion could be written

The forces include the inward spring force and the centrifugal force in this rotating frame of reference.

The spring force and centrifugal force are radial. Therefore, rather than trying to develop the equations above, I would express both forces in terms of r, and solve the differential equation for r(t).

where

You did not say if the angular velocity is constant. The angular velocity versus time will determine what the centrifugal force looks like and will determine theta versus time. Once you know r(t) and theta(t), convert to x(t) and y(t) in the standard way. If the angular velocity is constant then it is pretty easy. If the initial angle is not specified, you might as well assume angle theta=0 at t=0.

That should be enough hints to get you going.