Solution of the undamped unforced oscillator

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Reference no: EM132101884

Here is a formula for the solution of the undamped unforced oscillator 

y''[t] + 25. y[t] = 0

You can damp this oscillator lightly by adding a modest damping term b y'[t]:

Your mission is to keep c as defined above and find the critical value bcritical so that if 0 < b < bcritical, then the oscillator y''[t] + b y'[t] + c y[t] = 0 is not overdamped (i.e. its solution formulas have sines and/or cosines), but if bcritical < b, then the oscillator y''[t] + b y'[t] + c y[t] = 0 is overdamped (i.e. its solution formulas have no sines or cosines).

Reference no: EM132101884

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