Having Trouble Setting up a System...

...of DEs in regards to a written problem we've been given. Here it is, followed by a tentative 'stab' at what is meant to be in the equation.

"Suppose that the time rate of change **(ROC)** of a price M(t) of a product, minus inflation I(t) is proportional to the difference between Supply S(t) at time t and some equilbrium supply t.

(If the supply is too large and cost 'will' decrease. If supply is too low and price 'will' increase)

Also assume that the ROC in supply is proportional to the difference between the price P and some equilibrium

(If the price is too high and supply will increase. If the price is too low and supply will decrease)

We've also got that F(t) = sin*wt*

Now, this is what I have scribbled down in an attempt to get some working out, but I highly doubt that it is anywhere near correct, as I'm having trouble moving the knowledge of DEs from just straight questions into drawing stuff out of problems.

) = 0

I(t) = sin*wt*

As I've, I'm well from confident about it :( Can anyone help out at all? TYVM