Question

Problem 1. Find the natural frequency $omega_n$, damping ratio $zeta$, and impulse response $y_i(t)$ for the following transfer functions: (a) $G(s) = frac{s - 5}{s^2 + 15s + 50}$, (b) $G(s) = frac{10s + 20}{s^2 + 2s + 5}$. Furthermore, indicate whether each transfer function is undamped, underdamped, critically damped, or overdamped. Remember that the impulse response is $y_i(t) = mathcal{L}^{-1}{G(s)hat{u}(s)}$, where $u(t)$ is the delta function. Note: You can check your answers in Matlab. Use the 'tf' command to generate the transfer function, and use the 'impulse' command to generate the impulse response.

          Problem 1. Find the natural frequency $omega_n$, damping ratio $zeta$, and impulse response $y_i(t)$ for the following transfer functions:

(a) $G(s) = frac{s - 5}{s^2 + 15s + 50}$,

(b) $G(s) = frac{10s + 20}{s^2 + 2s + 5}$.

Furthermore, indicate whether each transfer function is undamped, underdamped, critically damped, or overdamped. Remember that the impulse response is $y_i(t) = mathcal{L}^{-1}{G(s)hat{u}(s)}$, where $u(t)$ is the delta function.

Note: You can check your answers in Matlab. Use the 'tf' command to generate the transfer function, and use the 'impulse' command to generate the impulse response.

$Problem 1. Find the natural frequency omegan, damping ratio zeta, and impulse response yi(t) for the following transfer functions: (a) G(s) = fracs - 5s^2 + 15s + 50, (b) G(s) = frac10s + 20s^2 + 2s + 5. Furthermore, indicate whether each transfer function is undamped, underdamped, critically damped, or overdamped. Remember that the impulse response is yi(t) = mathcalL^-1G(s)hatu(s), where u(t) is the delta function. Note: You can check your answers in Matlab. Use the 'tf' command to generate the transfer function, and use the 'impulse' command to generate the impulse response.$

Added by Antonio W.

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