Undamped force oscillation formulas

[gmmstr827]

Apparently the solution to the formula for undamped force oscillation mx''+kx=F0*cos(ωt) is x(t)=C*cos(ω0*t-α)+[(F0/m)/(ω0^2-ω^2)]*cos(ωt) where C is a constant, but are there any websites that show that derivation in an easy-to-follow way? I've tried Googling both the formulas and the topic, but I can't come up with anything. I need to use these formulas and seeing this would really help. If someone could provide a link or post it if they have it somewhere handy, that would be great.
Thank you.

 

[AlephZero]

For this specific equation, try googling for "response of single degree of freedom (or SDOF) dynamic systems".

Or if you want the general theory, look for "solving linear differential equations with constant coefficients".

There are lots of sites on those topics - which one is best for you depends how much math and/or physics you know already.

 

[gmmstr827]

Okay, thanks. I'm really only looking for the mathematical step-by-step derivation of it. I don't need a bunch of explanations, I can figure out problems by referring back to the general steps.