Question: 8) (15 points) Consider the simple model for a periodically forced mass (with mass m ) connected to a spring with spring constant k=100 :

8) (15 points) Consider the simple model for a periodically forced

8) (15 points) Consider the simple model for a periodically forced mass (with mass m ) connected to a spring with spring constant k=100 : y+m100y=sin(2t) a) Write down the general solution to the homogeneous problem (f(t)=0) for any value of m. b) For the forced problem, what value of m will result in the highest amplitude motion? In other words, what value of m causes resonance? Why? c) For this special value of m, what is the FORM of the particular solution, yp(t) ? (NO NEED TO CALCULATE the COEFFICIENTS.)

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