Solve the Next second order system Draw the electric circuit and assign the RLC values with the differential equation data. Solve with the natural and forzed answer.
Solve the Next second order system Draw the electric circuit and assign the RLC values with the differential equation da...
(2) a) An RLC circuit has the following differential equation (DE) for t > 0. d’v(t)/dt + 10 dv(t)/dt + 16 v(t) = 0) Determine the value of the damping ratio 5, the type of damping, and the form of the natural response for t > 0. Include all values where possible. (7 pts.) b) An RLC circuit has the following differential equation (DE) for t> 0. d’i(t)/dt? +4 di(t)/dt + 9 i(t) = 0 Determine the value of the...
A second-order RLC circuit is shown in Fig. 1 0.05F 3Ω 2Ω 6A 6A 5H Fig.1 A second-order RLC circuit with a switch (1) Analytical part: derive the differential equations and solve them to find the response i(t for t>0. Specify whether it is an underdamped, critically damped or overdamped case. A second-order RLC circuit is shown in Fig. 1 0.05F 3Ω 2Ω 6A 6A 5H Fig.1 A second-order RLC circuit with a switch (1) Analytical part: derive the differential...
Section 3: Laplace transform for RLC circuit analysis (10 marks) A second-order RLC circuit with a dependent source is shown in Fig. 3. 22 + VO - 132 1F + 15e-2 u(t) V ) 9[1-u(t)] V Y 0.50 » Fig. 3 A second-order RLC circuit with a dependent source Take the Laplace transform of the circuit and hence find the response io(t) for t > 0. Specify whether it is an underdamped, critically damped or overdamped case. Sketch the response.
1) Derive the 2d order differential equation for the circuit and solve the equation for a natural response and a forced response using initial conditions. Do not use Laplace Transforms. After finding the differential equation, classify the system as critically damped, overdamped, or underdamped and derive the response equation. 12 V 20㏀ 10 mH
2. a) (7 pnts) Solve the second order homogeneous linear differential equation y" - y = 0. b) (6 pnts) Without any solving, explain how would you change the above differential equation so that the general solution to the homogeneous equation will become c cos x + C sinx. c) (7 pnts) Solve the second order linear differential equation y" - y = 3e2x by using Variation of Parameters. 5. a) (7 pnts) Determine the general solution to the system...
shown below. (10 points). rmine the differential equation relating vi) and vot) for the RLC circuit i(t) C-0.5 F v(t) V,(t) b.. Suppose that avo(t) vi(t) e-3t u(t). Determine vdt) for t > 0 if vo(0-)-1 and 1 t-o-=2. (10 points). at
3 Draw the circuit at too and force i(0*) and ve(0*). Then solve for v(0*) and 4c(O*). Find the second intial condition given as 2 (7) 3- Draw the circuit at tm Replace the inductor with short circuit, and the capecitor with open circuit Then sove for 4i (o) and v (oo). Once the three values are obtained, you have two initial conditions to solve for A and B. In this lab, you will build a parallel RLC circuit shown...
Problem 3 A system is described by the following second-order linear differential equation d'y dz 5y(sin2t+ e-t)u(t) dt2 where y(0)y()0 Solve the differential equation using the Laplace Transform method.
Rewrite the second order differential equation, as a system of a first order differential equation. (see picture) det + sin(a) = 0, 6(0) = el 10) = 0, += [0, 1] 2012 0, t=
2. Coupled Differential Equations (40 points) The well-known van der Pol oscillator is the second-order nonlinear differential equation shown below: + au dt 0. di The solution of this equation exhibits stable oscillatory behavior. Van der Pol realized the parallel between the oscillations generated by this equation and certain biological rhythms, such as the heartbeat, and proposed this as a model of an oscillatory cardiac pacemaker. Solve the van der Pol equation using Second-order Runge Kutta Heun's method with the...