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Resonance is not a phenomenon reserved for undamped mechanisms. Re-consider the mass-spring example from class with the additional constraint that the system is subject to 2 Newtons per meter per second of damping. Suppose the system undergoes periodic forcing of the form cos( omega t) where omega is as yet undetermined. That is to say, consider the following example: d2x/dt2 + 2 dx/dt + 4x (t) = cos(omega t).(1) [Hint: See Chapter 5.6, Example 6 for help.] Find the general solution of (1). [Hint: Note that we do not need to consider cases for omega !]
Show transcribed image text Resonance is not a phenomenon reserved for undamped mechanisms. Re-consider the mass-spring example from class with the additional constraint that the system is subject to 2 Newtons per meter per second of damping. Suppose the system undergoes periodic forcing of the form cos( omega t) where omega is as yet undetermined. That is to say, consider the following example: d2x/dt2 + 2 dx/dt + 4x (t) = cos(omega t).(1) [Hint: See Chapter 5.6, Example 6 for help.] Find the general solution of (1). [Hint: Note that we do not need to consider cases for omega !]