Question: Use dashpot system given by my + by ' + ky = F ( t ) y ( 0 ) = 0 , y

Use dashpot system given by my"+by'+ky=F(t) y(0)=0, y'(0)=0. Being rearranged we have y"=(F(t))/m-b/m y'-k/m y. Please do the analytical part
Use dashpot system given by my

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