1) a) Use the method of undetermined coefficients to find the forced response (initial conditions are...

 

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1) a) Use the method of undetermined coefficients to find the forced response (initial conditions are zero) to a single degree of freedom mass-spring system with the following equation of motion: * + 9x = 3 cos (3t). b) Sketch the response you found in part a and comment on how amplitude and period of forced oscillations change in time, and what is the phase shift between forcing and response? c) When damping is added to the system, what happens to amplitude and period of forced oscillations? What happens to the phase shift? Please answer qualitatively (no need to find forced response for the damped oscillator 1) a) Use the method of undetermined coefficients to find the forced response (initial conditions are zero) to a single degree of freedom mass-spring system with the following equation of motion: * + 9x = 3 cos (3t). b) Sketch the response you found in part a and comment on how amplitude and period of forced oscillations change in time, and what is the phase shift between forcing and response? c) When damping is added to the system, what happens to amplitude and period of forced oscillations? What happens to the phase shift? Please answer qualitatively (no need to find forced response for the damped oscillator