Method of undertermined coefficients

[lordy12]

Homework Statement

The motion of an undamped mass-spring system is described by the differential equation 2x" + 36x = sin(wt)

a) For what values of w will the system exhibit resonance?
b) Use the method of undertermined coefficients to find a particular solution in the case where w is not the resonant frequency.





I know I have to use y = Asin(wt) but I am stuck after that.

 

[ideasrule]

Do you know how to solve a second-order differential equation? First you solve the corresponding homogeneous equation, then find a particular solution, then add the two. You may find it easier to do a) after doing b).