For each of the second-order systems that follow, find damping ratio 7 , natural frequency @r, Ts, Tp, Tr , and %OS. 16 T(s) = g2 + 3s + 16 0.04 T(s) : +0.02s+0.04

Design a circuit that will amplify 1.3V sin(5Pi6000t) to a value of -13V sin (5Pi6000t). Use realistic component values. Will the circuit have clipping?

A series RLC circuit is connected to a 25 V source of variable frequency. The circuit current is found to be a maximum of 0.5 A at a frequency of 400 Hz and the voltage across C is 150 V. Assuming ideal components, the values of R and L are respectively ?

Charging Capacitor: For a charging capacitor the Kirchoff's Loop Rule gives R E – IR C ww C In this case the current is entering the positive plate so I = dQ/dt = CdAVc/dt and we get dVc E – RC - Vc = 0 dt The solution to the differential equation is V.(t) = E (1 – e-t/(RC)) (charging capacitor) Notice that V.(0) = 0 and V.(0) = E as we expect for a charging capacitor. 5. You can easily find the time constant if you are given a graph of voltage across a charging capacitor as a function of time. Whent = RC, the voltage across the capacitor is V.(t = RC) = E(1 – e-1) × 0.63 E. Therefore the time constant is just how long it takes for AV(t) to reach 63% of the EMF. The graph shows the voltage across a charging capacitor as a function of time. The resistance of the circuit is 7.5 kN. а. Determine the capacitance of the capacitor. 10 8 60 40 time (ms) 20 80 100 b. What is the current at t = 10 ms? Hint: the easiest way to do this is to use the loop rule. (volts) 4.