a) Given the following system below Where wwwm S X(t) dy(t) dt S +y(t)= x(t) and...

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a) Given the following system below Where wwwm S₁ X(t) d²y(t) dt² S₁ +y(t)= x(t) and S₂ Find the transfer function of the system b) Given the following block diagram 1/m D Y(t) K₂ $₂ = Z(1) dz(t) dt c) prove that the roots for this system are -1-j and -1+j Y(s) R(s) S²+2çwnS + w/7/2 T 6z = dy(t) dt derive the differential equation relating the output c(t) to the input r(t) c(t) when ts (settling time for the 5 percent criterion) is 3 and the percent overshoot Mp is 4.3% a) Given the following system below Where wwwm S₁ X(t) d²y(t) dt² S₁ +y(t)= x(t) and S₂ Find the transfer function of the system b) Given the following block diagram 1/m D Y(t) K₂ $₂ = Z(1) dz(t) dt c) prove that the roots for this system are -1-j and -1+j Y(s) R(s) S²+2çwnS + w/7/2 T 6z = dy(t) dt derive the differential equation relating the output c(t) to the input r(t) c(t) when ts (settling time for the 5 percent criterion) is 3 and the percent overshoot Mp is 4.3%