

3. (30 points) Critically-damped - Determine vo(t)! 200 10uH Vo(t) i(t) v(t) 1Vu(t) 100nF
In the critically damped circuit shown in the figure below, the
initial conditions on the storage elements are
iL(0) = 2 A and
vC(0) = 5 V. Determine the voltage
v(50 ms).
Please show all work, thank you.
In the critically damped circuit shown in the figure below, the initial conditions on the storage elements are i(0) = 2 A and vc0) = 5 V. Determine the voltage v(50 ms). + + il(0) vc( 0+ 0.01 F v(t) 3 1002...
Problem #3 a) Determine if the next second order system is oscillating, low damped, critically damped or overdamped. Justify your conclusion. G(s)10 s2 +s +1 b) Determine the maximum percentage overdrive (if any) and the set time to the 2% criterion that will have the response to the unit step of the previous system. c) Plot the response to the magnitude 5 step of the G (s) system.
Problem 4. The Fast Decay of Critically Damped Simple Harmonic Oscillator. A simple harmonic oscillator (a box with mass m attached to a Hook's spring of coefficient k with linear air friction of coefficient n) is described by mx"(t) + n2'(t) + ku(t) = 0 where m, n, k > 0. (a) Write down the solutions for three cases and their long term limits 1. Overdamped: when friction is strong 1 > 4mk 2. Underdamped: when friction is weak 72...
Determine if overdamped,underdamped, or critically damped
For the circuit shown below, Vs-200V, R-30, R.-50. C -0.125pF and L-SmH. Find (a) the initial voltage across the capacitor 20. (b) the initial current through the inductor, lu(0). (e) the damping coefficient and resonant frequency . (d) the initial condition dvede , (e) the voltage across the capacitor (t) for the initial condition diu/dt , and the current through the inductor lu(t) for p R2 Voc
2) a) Derie weayti for the critically damped case, 5-1. b) Determine the position, velocity and acceleration error constants for the forward-path 4(s+2 s" (s+5) transfer function given by G(s)-- c) Determine the steady-state errors of the unit feedback system with the forward-path paroc i ansfer funcioo given ru n
2) a) Derie weayti for the critically damped case, 5-1. b) Determine the position, velocity and acceleration error constants for the forward-path 4(s+2 s" (s+5) transfer function given by G(s)--...
Calculate vo(t) in the circuit shown in the figure below if i(t) is 200 cos(105t+ 60°) mA, i2(t) is 100 sin(105t90°) mA, and vst) 10 sin(105t) v uci) + 250 nF o(r) 52 Ohm
Calculate vo(t) in the circuit shown in the figure below if i(t) is 200 cos(105t+ 60°) mA, i2(t) is 100 sin(105t90°) mA, and vst) 10 sin(105t) v uci) + 250 nF o(r) 52 Ohm
Problem 4 Problem 3 (35): The particle with mass m is initially at equilibrium. The cord is assumed to be taut throughout the motion. The system is critically damped with parameters are m = 4 kg and k = 200 N/m. 7n a) (15) Determine the value of the viscous damping coefficient c. b) (10) If at t -0 the mass m is displaced down the incline by a distance xo -0.2 m from the equilibrium position and released with...
(1 point) This problem is an example of critically damped harmonic motion. A mass m = 6 kg is attached to both a spring with spring constant k = 150 N/m and a dash-pot with damping constant c = 60 N· s/m . The ball is started in motion with initial position Xo = 8 m and initial velocity vo = -42 m/s. Determine the position function x(t) in meters. x(t) = Graph the function x(t). Now assume the mass...
5. For each of the following, determine if the system is underdamped, undamped, critically damped or overdamped ad sketch the it step response (a) G (s) = (c) G(s)-t 2+68+ (d) G (s) = 36 6. The equation of motion of a rotational mechanical system is given by where θ° and θί are respectively, output and input angular displace- ments. Assuming that all initial conditions are zero, determine (a) the transfer function model. (b) the natural frequency, w natural frequency,...
5. For each of the following, determine if the system is underdamped, undamped, critically damped or overdamped ad sketch the it step response (a) G (s) = (c) G(s)-t 2+68+ (d) G (s) = 36 6. The equation of motion of a rotational mechanical system is given by where θ° and θί are respectively, output and input angular displace- ments. Assuming that all initial conditions are zero, determine (a) the transfer function model. (b) the natural frequency, w natural frequency,...