Problem $1$:

Determine the $75\%$ response time of the following first order system $($assume zero initial conditions$)$

$0\mathrm{.}4T^{}+T=4U(t)$

Problem $2$:

The frequency response of a first order system is represented by the following figure:

$1-$ Determine the static gain K

$2-$ Determine the time constant $.$

$3-$ Determine the Cutoff frequency $f_c$ of this system.

$4-$ Estimate the instrument's usable frequency range to keep its dynamic error within $50\%.$

$5-$ We excite the system with a sinusoidal signal $e(t)=4sin(2Ft)$ where $F=20Hz.$ Calculate the maximum value of the output signal and the phase shift.