The signal $$\cos\;\omega_ct\;+\;0.5\;\cos\;\omega_mt\;s\mathrm{in}\;\omega_ct$$ is

The magnitude of frequency response of an underdamped second order system is 5 at 0 rad/sec and peaks to $${{10} \over {\sqrt 3 }}$$ at 5 $$\sqrt 2 $$ rad/sec. The transfer function of the system is

A certain system has transfer function $$G\left(s\right)=\frac{s+8}{s^2+\alpha s-4}$$, where $$\alpha$$ is a parameter. Consider the standard negative unity feedback configuration as shown below Which of the following statements is true?

Group I lists a set of four transfer functions. Group II gives a list of possible step responses y(t). Match the step responses with the corresponding transfer functions

Group I $$$P=\frac{25}{s^2+25}\;\;\;\;\;Q=\frac{36}{s^2+20s+36}$$$ $$$R=\frac{36}{s^2+12s+36}\;\;\;\;\;S=\frac{49}{s^2+7s+49}$$$

Group II