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Consider the differential equation u ′′ + bu = sin^2 (2t). (a) For what value of...

Consider the differential equation u ′′ + bu = sin^2 (2t).

(a) For what value of b does the solution show resonance? Clearly, explain your answer. Hint: sin2 x = 1−cos(2x) 2

(b) Consider the same differential equation but take the non-homogeneous term to be sin4 t. For what value(s) of b does the solution show resonance? You do not have to give an exact solution but you do have to explain clearly your thinking using the structure of the equation.

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