Mechanical Vibrations Differential Equation

[Goatsenator]

Homework Statement

Find the general solution for the differential equation

Homework Equations

y'' + 16y = tan(4t)

The Attempt at a Solution

I get C₁cos(4t) + C₂sin(4t) = 0 for my homogeneous equation.

I did the usual method of undetermined coefficients (I think I took all of the derivatives correctly). However I'm getting something strange for y_p. I can't really make sense of the solution. Does this have something to do with the fact that the tangent function has discontinuities? Would this be some kind of resonance?

 

[rock.freak667]

There is no sort of 'fixed' form for the PI of tan(4t), you might need to try variation of parameters to solve it.

 

[Goatsenator]

Oh yeah! Thanks for the help!