How do you solve a nonhomogeneous second order ODE with a cosine function?

[Stu165]

Can anyone give me a hand with this, cause I'm stumped and can't remember exactly how to go about solving this.

here's the eqn

m[d^2x/dt^2 + wsubo^2 x] = F cos wt

I'm supposed to show that x(t) = xsubo cos wt

w is the incident freq
wsubo is the resonant freq
m is mass

it's from physics but the principles are just maths.

 

[Euclid]

Since you are given the solution, just plug it into the eqn. I get a solution only when x_0=\frac{w^2-F}{w^2}.

 

[Stu165]

I would have thought you would have to work with undetermined coefficients or something

 

[dextercioby]

PLEASE,DO NOT DOUBLE POST!

Daniel.

 

[HallsofIvy]

I would have thought you would have to work with undetermined coefficients or something

No, you were not asked to SOLVE the equation, only to show that
x(t) = x₀ cos wt IS a solution.

 

[Stu165]

I just found this out, by plugging in xsubocoswt, I got F = m (wsub0^2 - w^2) x

by then using undetermined coefficients I get a value of

y(t) = F / m (wsub0^2 - w^2) coswt

by substituting F in I get the xcos wt