Final answer:
To find the percent overshoot, settling time, rise time, and peak time for a third-order system with a given transfer function, we need to first determine if we can use the second-order approximation. Then, we can find the roots of the characteristic equation and use them to calculate the desired parameters.
Step-by-step explanation:
To find the percent overshoot, settling time, rise time, and peak time for a third-order system with a transfer function T(s), we need to determine if we can use the second-order approximation. For a third-order system, if the damping ratio is small and the natural frequency is high, we can use the second-order approximation. The transfer function T(s) = 14.65 / (s^2 + 0.842s + 2.93)(s + 5) is a third-order system, so we cannot use the second-order approximation. To find these parameters, we need to find the roots of the characteristic equation by setting the denominator of the transfer function equal to zero.
Setting s^2 + 0.842s + 2.93 = 0, we can use the quadratic formula to solve for the roots. The roots are complex conjugate and can be written as s = -0.421 + 1.89j and s = -0.421 - 1.89j. The percent overshoot, settling time, rise time, and peak time can be calculated using these roots.