I have this study guide for an upcoming test for DE class I'm trying to figure out.
A mass of 400 grams stretches a spring by 5 centimeters.
(a) Find the spring constant k, the angular frequency ω, as well as the period T and frequency f of free undamped motion for this spring-mass system.
(b) Find the general solution of the DE for the free spring-mass system.
(c) Suppose that an exterior force of F(t) = 27sin(13t) Newtons
acts on the spring-mass system. Find the equation of motion of the system if the mass initially is at rest in its equilibrium position.
I know K is 784 (or do I need to convert to 5 centimeters to 0.05 meters?) and w is sqrt(k/m), but I'm not sure what I need to find T and F. I can find the general solution, but then I have no clue on what to do with part c.