Question

The transfer function of a control system is given by:
$\frac{C\left(s\right)}{R\left(s\right)}=\frac{25}{s^2+6s+25}$
The first maximum value of the response occurs at a time $t_{max}$ given by

• A. $\frac{\pi }{8}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{2}$
• D. $\pi$

Answer 1

The correct option is B $\frac{\pi }{4}$

$t_{max}$ is the peak time $\left(t_p\right)$

${\omega }_n=5,\zeta =0.6$

$t_p=\frac{n\pi }{{\omega }_n\sqrt{(1-{\zeta }^2)}}$

first maxima is at n = 1

$\therefore t_{max}=\frac{\pi }{5\sqrt{1-(0.6{)}^2}}=\frac{\pi }{5\times 0.8}=\frac{\pi }{4}$