Pg 6 TTG1401/TG1401 Question 2 (25 marks) For a RCL circuit, the current I d2I(t) dl(t) 1 dt C is governed by the differential equation, dt2 V1 and V2 are constants. Solve the above differential...
1 2 9. The diagram below is an RCL circuit with R = 10 ohms, C = 10-2farad, L henry, and V = 12 volts. The switch is closed at time t = 0. Assume that the initial current i(0) = 0 and the initial charge on the capacitor Q(0) = 0 . Find the current i = i(t) in the circuit if i satisfies the equation and, according to Kirchhoff's law, ai lezo = R di d2i dt2 +...
1 2 9. The diagram below is an RCL circuit with R = 10 ohms, C = 10-2farad, L henry, and V = 12 volts. The switch is closed at time t = 0. Assume that the initial current i(0) = 0 and the initial charge on the capacitor Q(0) = 0 . Find the current i = i(t) in the circuit if i satisfies the equation and, according to Kirchhoff's law, ai lezo = R di d2i dt2 +...
Solve the following differential equation using
variation of parameters.
d yt) 2 dy() +7- + 10y() u(t) dt dt2 y(0) 0, y'(0) = 3
d yt) 2 dy() +7- + 10y() u(t) dt dt2 y(0) 0, y'(0) = 3
I need help with question
#3
When there is no fishing, the growth of a population of clown fish is governed by the following differential equation: dy dt 200 where y is the number of fish at time t in years. 1. Solve for the equilibrium value(s) and determine their stability. Create a slope field for this differential equation. Use the slope field to sketch solutions for various initial values. 2. 3. Summarize the behavior of the solutions and how...
I need help solving this problem.
Vi V2 Problem 1) Show steps below to solve V1 and V2 using Nodal Analysis i) Write equation for controlling current I, in terms of node voltage V2 [2] 21 2 ΚΩk 8 kΩΣ 4 ΚΩΣ ii) Write KVL equation for Supernode source [1] iii) Write Node equation for V, and simplify in terms of V, and V2 [2] iv) Write Node equation for V2 and simplify in terms of V, and V2 [2]...
suppose an input voltage is given as V(t) = 240[u(t-5) - u(t-10)]. In a branch of an electronic circuit, the variation of current with time is modeled by the differential equation d^2(i)/dt^2 + 36i = dv/dt. Assuming zero initial conditions, determine I as a function of t. (hint: use laplace transforms)
solve
Question 6: Given that v(0) = 2 and dv(0)/dt = 4, solve the following second-order differential equation d- du ( +54 + 60 = 10e-'u(t) dt 4 marks
Differential Equations: Given that λ1= 6, v1=(1,1) and λ2=−2, v2=(1−1) are eigenpairs of A, solve x′=Ax, x(0) =k. (Ans:~x=(e6t)(3,3)+e^(−2t)(−6,6)) This is the answer but not sure how to get there.
can
you post the answer in matlab and code
Question 1: Euler's Method. A simple circuit having resistance R, in- ductance L, and capacitance C in parallel has a current i(t) that satisfies the differential equation 1 dV + R dt V di C dt2 www. dt Take parameters C 0.3 farads, R assume that the applied voltage to the circuit is given by 1.4 olms, andL= 1.7 henries and -0.06t sin(2t). V (t) e Using Euler's method, approximate the...
Answer all questions (100 marks) 1. Given x(0) = 0 and transform. = 0, solve the following differential equation using Laplace d?x(t) dx +6 dt2 + 8x(t) = 2e-31 dt (20 marks) 2. Find the vo(t) in the network in Figure I using Laplace approach. 12 S 2 w O 1,(s) Ls) V.(5) Figure 1 (30 mrks)