Mechanical Vibrations Differential Equation

AI Thread Summary
The discussion centers on solving the differential equation y'' + 16y = tan(4t). The user successfully found the homogeneous solution as C1cos(4t) + C2sin(4t) but is struggling with the particular solution. They express confusion regarding the application of the method of undetermined coefficients due to the discontinuities of the tangent function. The user considers whether resonance might be a factor and suggests that variation of parameters could be necessary to find the particular integral. The conversation highlights the challenges posed by the tangent function in this context.
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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 yp. 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?
 
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There is no sort of 'fixed' form for the PI of tan(4t), you might need to try variation of parameters to solve it.
 
Oh yeah! Thanks for the help!
 
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