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.
Best Answer
You don't need to convert because your units of mass are grams, so you are using CGS system of units. For a: $\omega=2 \pi/T$ For c: You have to add the new force to Newton's law.