Consider the forced damped mechanical system y + 8y + 17y=1-e-4t, where y(t) is the displacement...

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Consider the forced damped mechanical system y" + 8y + 17y=1-e-4t, where y(t) is the displacement at time t and the right hand side corresponds to a non-oscillatory force that is gradually applied. (a) Find the general solution of the associated homogeneous equation Note: Use "A" and "B" as your arbitrary constants. Yh (t) = Yp (t) (b) Use the method of undetermined coefficients to find a particular solution of (1). = (c) Hence find the solution of (1) subject to the initial conditions y(0) = 0 and y' (0) = 0. y(t) = (d) As time t→→→→→∞, determine the behaviour of the forcing function and your solution y(t) in part (c) above. y" + 8y' +17y = 0. F(t) y(t) → 1 1/20 F(t)=1-e-4t (1) Consider the forced damped mechanical system y" + 8y + 17y=1-e-4t, where y(t) is the displacement at time t and the right hand side corresponds to a non-oscillatory force that is gradually applied. (a) Find the general solution of the associated homogeneous equation Note: Use "A" and "B" as your arbitrary constants. Yh (t) = Yp (t) (b) Use the method of undetermined coefficients to find a particular solution of (1). = (c) Hence find the solution of (1) subject to the initial conditions y(0) = 0 and y' (0) = 0. y(t) = (d) As time t→→→→→∞, determine the behaviour of the forcing function and your solution y(t) in part (c) above. y" + 8y' +17y = 0. F(t) y(t) → 1 1/20 F(t)=1-e-4t (1)