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dx dt 1. For the circuit below determine: a) The initial conditions: iz(0+), dix(0*), v(0+), dv(0+)...
2. For the circuit in problem 1 above: a) Transform the circuit into the s-domain b)...
2. For the circuit in problem 1 above: a) Transform the circuit into the s-domain b) Using Laplace transform techniques applied directly to the circuit (not applied to the differential equation found in problem 1), find iz(t), t > 0. No credit for time- domain techniques. IX V 40 + - 5+10u(t) 10 H 1/4 F 2. For the circuit in problem 1 above: a) Transform the circuit into the s-domain b) Using Laplace transform techniques applied directly to the...
Solve the following differential equation using the Laplace transform and assuming the given initial conditions. [Note:...
Solve the following differential equation using the Laplace transform and assuming the given initial conditions. [Note: Laplace table is provided in the page 6] dt2 dt dix x(0) = 1 ; (0) = 1 dt
Sheet1 Control 1. Solve the following differential equations using Laplace transforms. Assume zero initial conditions dx...
Sheet1 Control 1. Solve the following differential equations using Laplace transforms. Assume zero initial conditions dx + 7x = 5 cos 21 di b. + 6 + 8x = 5 sin 31 dt + 25x = 10u(1) 2. Solve the following differential equations using Laplace transforms and the given initial conditions: de *(0) = 2 () = -3 dx +2+2x = sin21 di dx di dx di 7+2 x(0) = 2:0) = 1 ed + 4x x(0) = 1:0) =...
Solve the system of differential equations dx/dt = x-y, dy/dt = 2x+y subject to the initial conditions x(0)= 0 and y(0) = 1.
Solve the system of differential equations dx/dt = x-y, dy/dt = 2x+y subject to the initial conditions x(0)= 0 and y(0) = 1.
solve Question 6: Given that v(0) = 2 and dv(0)/dt = 4, solve the following second-order...
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
(6). The quantities x(t) and y(t) satisfy the simultaneous equations dt dt dx dt where x(0)-y(0)-...
(6). The quantities x(t) and y(t) satisfy the simultaneous equations dt dt dx dt where x(0)-y(0)-ay (0)-0, and ax (0)-λ. Here n, μ, and λ are all positive real numbers. This problem involves Laplace transforms, has three parts, and is continued on the next page. You must use Laplace transforms where instructed to receive credit for your solution (a). Define the Laplace Transforms X(s) -|e"x(t)dt and Y(s) -e-"y(t)dt Laplace Transform the differential equations for x(t) and y(t) above, and incorporate...
8.43 The initial conditions for the circuit shown in Figure P8.43 are i(0) = 1 =...
8.43 The initial conditions for the circuit shown in Figure P8.43 are i(0) = 1 = 1 A, v(0) = V. = 2 V. FIGURE P8.43 w 40 a. Write a node equation at node a by summing the currents leaving node a fort 20. Find di(0)/dt. b. Write a node equation at node b by summing the currents leaving node b for t 2 0. c. Find the differential equation in i(t) and find the roots of the characteristic...
use the Euler method to solve the differential equation : dv/dt = ve^(1+t)+0.5v for t, between...
use the Euler method to solve the differential equation : dv/dt = ve^(1+t)+0.5v for t, between 0 and 0.2, in steps of 0.02; with the initial condition, v=1 when t=0. Compare your results to the excel analytical solution in tabular and graphical forms
Please do the problem if you can do ALL parts. t-0 a SW1 SW2 0.5 Ω 2 1Ω V. R3 20 A T v(t) 0.5 F 0.5 H 0 Find the initial current i(0) through the inductor and the initial voltage v(0) across the capa...
Please do the problem if you can do ALL parts.
t-0 a SW1 SW2 0.5 Ω 2 1Ω V. R3 20 A T v(t) 0.5 F 0.5 H 0 Find the initial current i(0) through the inductor and the initial voltage v(0) across the capacitor at t 0. b. Write a node equation at node a fort2 0. c. Represent v(t) as a function of i(t) on the series connection of R2 and L. Find dv(t)/dt. Derive a second-order differential...
(1 point) An object of mass 5 kg is given an upward initial velocity of 16...
(1 point) An object of mass 5 kg is given an upward initial velocity of 16 m/sec and then allowed to fall under the influence of gravity. Assume that the force in newtons due to air resistance is -50, where v is the velocity of the object in m/sec. Assume gravitational constant is g = 9.8m/seca. Set up the differential equation for this scenario: v' = m/sec Solve the differential equation for the equation of motion: The equation is both...
2. For the circuit in problem 1 above: a) Transform the circuit into the s-domain b) Using Laplace transform techniques applied directly to the circuit (not applied to the differential equation found in problem 1), find iz(t), t > 0. No credit for time- domain techniques. IX V 40 + - 5+10u(t) 10 H 1/4 F 2. For the circuit in problem 1 above: a) Transform the circuit into the s-domain b) Using Laplace transform techniques applied directly to the...
Solve the following differential equation using the Laplace transform and assuming the given initial conditions. [Note: Laplace table is provided in the page 6] dt2 dt dix x(0) = 1 ; (0) = 1 dt
Sheet1 Control 1. Solve the following differential equations using Laplace transforms. Assume zero initial conditions dx + 7x = 5 cos 21 di b. + 6 + 8x = 5 sin 31 dt + 25x = 10u(1) 2. Solve the following differential equations using Laplace transforms and the given initial conditions: de *(0) = 2 () = -3 dx +2+2x = sin21 di dx di dx di 7+2 x(0) = 2:0) = 1 ed + 4x x(0) = 1:0) =...
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
(6). The quantities x(t) and y(t) satisfy the simultaneous equations dt dt dx dt where x(0)-y(0)-ay (0)-0, and ax (0)-λ. Here n, μ, and λ are all positive real numbers. This problem involves Laplace transforms, has three parts, and is continued on the next page. You must use Laplace transforms where instructed to receive credit for your solution (a). Define the Laplace Transforms X(s) -|e"x(t)dt and Y(s) -e-"y(t)dt Laplace Transform the differential equations for x(t) and y(t) above, and incorporate...
8.43 The initial conditions for the circuit shown in Figure P8.43 are i(0) = 1 = 1 A, v(0) = V. = 2 V. FIGURE P8.43 w 40 a. Write a node equation at node a by summing the currents leaving node a fort 20. Find di(0)/dt. b. Write a node equation at node b by summing the currents leaving node b for t 2 0. c. Find the differential equation in i(t) and find the roots of the characteristic...
Please do the problem if you can do ALL parts.
t-0 a SW1 SW2 0.5 Ω 2 1Ω V. R3 20 A T v(t) 0.5 F 0.5 H 0 Find the initial current i(0) through the inductor and the initial voltage v(0) across the capacitor at t 0. b. Write a node equation at node a fort2 0. c. Represent v(t) as a function of i(t) on the series connection of R2 and L. Find dv(t)/dt. Derive a second-order differential...
(1 point) An object of mass 5 kg is given an upward initial velocity of 16 m/sec and then allowed to fall under the influence of gravity. Assume that the force in newtons due to air resistance is -50, where v is the velocity of the object in m/sec. Assume gravitational constant is g = 9.8m/seca. Set up the differential equation for this scenario: v' = m/sec Solve the differential equation for the equation of motion: The equation is both...
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