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the input is to some differential equation D2x = Dx + x + Input

the input = sin(2pi * f * t)

so say I want to make a program that solves for the zero input frequency response. (Matlab actually)

what would I need to set the variable for frequency to be? would it be 1/(4t) ? to make the input always sin(pi/2) = 0? or do I make the frequency equal to zero.

I've been asking my workmates and getting mixed answers :[

I'm doing this for my research professor btw