Solve Spring Mass Problem: Get Help Now!

[DrMath]

Homework Statement

Hi PF frens,
I've got the attached picture translated into differential equation representation.
However, not so sure how the r(t) and f multiply dee-y / dee-t comes about.
Kindly advise?

Homework Equations

The Attempt at a Solution

see attached jpeg.

 

[fatra2]

Hi there,

From what I can see, the $$f \frac{dy}{dt}$$ seems to be the friction force applied on the system. I would guess r(t) the simple gravitational pull, but I might be mistaking.

Cheers