1. Find the zero-imput y.(t) for the following system if the initial condition is y (0)...

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1. Find the zero-imput y.(t) for the following system if the initial condition is y (0) =5, xa(0) =0, and y (0) =6 D (D+4D +3) y(t) 0 2. Find the zero-input ya(t) for the following system if the initial condition is y (0) = 1 and y (0)= 2 (hint: for repeat root, the characteristic mode is y,(t) (c +c,f)e") (D2+10D +25) y(t) = 0\ 3. Find the zero-input y. (t) for the following system if the initial condition is y(0) = 0 and y. (0) = 4. (hint: for complex roots 2 = atB, the characteristic mode is either %3D y.(t) = e" (c, cos Bt+c, sin ßr) or y,(t) = ce" cos( +0) (D+8D +20) y(t) =0 4. Find the zero-input y.(t) for the following system if the initial condition is ya (0) = 0, x (0) = 2, and ya (0) = 4 D (D2+8D +16) y(t) = 0 DFocus 1. Find the zero-imput y.(t) for the following system if the initial condition is y (0) =5, xa(0) =0, and y (0) =6 D (D+4D +3) y(t) 0 2. Find the zero-input ya(t) for the following system if the initial condition is y (0) = 1 and y (0)= 2 (hint: for repeat root, the characteristic mode is y,(t) (c +c,f)e") (D2+10D +25) y(t) = 0\ 3. Find the zero-input y. (t) for the following system if the initial condition is y(0) = 0 and y. (0) = 4. (hint: for complex roots 2 = atB, the characteristic mode is either %3D y.(t) = e" (c, cos Bt+c, sin ßr) or y,(t) = ce" cos( +0) (D+8D +20) y(t) =0 4. Find the zero-input y.(t) for the following system if the initial condition is ya (0) = 0, x (0) = 2, and ya (0) = 4 D (D2+8D +16) y(t) = 0 DFocus