![7. The charge Q-Q(t) on a capacitor as a function of time obeys the differential equation Q + Q = E(t). with the electromotive force E given by E)-cos(ut) here w >0 is a constant. (a) (2 points) Find Q(t) for all 0 t < π if Q(0)-Q(0) = 0. (b) (8 points) For wメ find Q(t) for all 12 π, assuming that Q and Q, are continuous at t = π. [Remark. Soon, you will be able to solve this problen in an elegant fashion using Laplace transforms and step functions, but for now you are asked to solve it without those tools.] (c) (5 points) Repeat part (b) for w = 1.](http://img.homeworklib.com/questions/a1cb81e0-77e4-11ea-a4e0-31804a34b098.png?x-oss-process=image/resize,w_560)
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7. The charge Q-Q(t) on a capacitor as a function of time obeys the differential equation...
Recall that the differential equation for the instantaneous charge q(t) on the capacitor in an RC-series...
Recall that the differential equation for the instantaneous charge q(t) on the capacitor in an RC-series circuit is dt C Use the Laplace transform to find the charge q(t) on the capacitor in an RC-series circuit subject to the given conditions q(0) = 0, R = 2.5 Ω, C = 0.08 , E(t) given in the figure below q(t) = E(t) 3 eBook
4. In lab 4 we consider the differential equation y" 2yywyF(t) for different forcing terms F(t). ...
Please answer parts c-d only.
4. In lab 4 we consider the differential equation y" 2yywyF(t) for different forcing terms F(t). In this problem we analyze this equation further using Laplace transforms 0, t<1 (a) Consider y" + y, +40y-1(t), where I(t)- t < 2. Find 1 1, 0. t>2 the forward transform Y-E(y) if y(0)-y(0)-0 (b) Solve y" + y, + 40y-1, y(0) = y'(0) = 0, using Laplace transforms Notice how the value of Y (s) you obtain...
1. Solve the boundary value problem ut =-3uzzzz + 5uzz, u(z, 0) = r(z) (-00 < z < oo, t > 0), usi...
1. Solve the boundary value problem ut =-3uzzzz + 5uzz, u(z, 0) = r(z) (-00 < z < oo, t > 0), using direct and inverse Fourier transforms U(w,t)-홅启u(z, t) ei r dr, u(z,t)-二U( ,t) e ur d . You need to explain where you use linearity of Fourier transform and how you transform derivatives in z and in t 2. Find the Fourier transform F() of the following function f(x) and determine whether F() is a continuous function (a)...
If = Q, where Q is a function of y only, then the differential equation M...
If = Q, where Q is a function of y only, then the differential equation M + Ny = 0 has an integrating factor of the form +(y) = es Q(u) dy Find an integrating factor and solve the given equation. ydx + (3xy - e-39) dy=0 Enclose arguments of functions in parentheses. For example, sin (22) To enter y in text mode, type (ly) or abs(y). Use multiplication sign in all cases of multiplication. The integrating factor is (y)...
problem 1) Find the differential equation describing the amount of salt,Qb, in the tank for times...
problem 1) Find the differential equation describing the
amount of salt,Qb, in the tank for times t in the interval t>=T.
Then solve to obtain Qb(t) for t>= T
A Water Tank Problem with Discontinuous Source A water tank contains V > 0 liters of pure water and Qo grams of salt. At time t = 0 we start pouring water into the tank with a rate r >0 liters per minute with a salt concentration of q> 0 grams...
y(t) is INCORRECT but x(t) is CORRECT DIFFERENTIAL EQUATIONS / Linear Algebra Only people that are...
y(t) is
INCORRECT
but
x(t) is CORRECT
DIFFERENTIAL EQUATIONS / Linear Algebra
Only people that are proficient in DIFFERENTIAL EQUATIONS should
even attempt to solve. No beginners or amateurs allowed.
Please write clearly and legibly. No sloppy Handwriting. I must
be able to clearly and easily read your solution and answer.
Circle final answer.
BELOW is an example of what the answer should look very similar
to. should be in the same form basically.
example
7.10.4 Question Help Use the...
I H C0 005 f Recall that the differential equation for the instantaneous charge g(0) on...
I H C0 005 f Recall that the differential equation for the instantaneous charge g(0) on the capacitor in an series circuit is LRC 2 dq 1 Use the Laplace transform (show all work on separate paper) when L = 1h, R-20 Ω, C= 0.005 f, E(t) 140 V, i> 0, q(0) 0, and i(0) 0 to find a) q(t)- b) What is the current i(t)?
The position x of a mass m attached to a spring obeys the differential equation i...
The position x of a mass m attached to a spring obeys the differential equation i + yi + w?x = 0 where y 2w. a) (2 marks) Write down expressions for the forces on the mass due to (i) the spring, and (ii) damping. (3 marks) Using a trial solution x = Ae"', show that a = --y/2 ± (y2/4 - «2)1/2 b) c) (4 marks) Show, by finding wd, that the solution is a damped oscillation of the...
2. Consider a thin rod of length L = π (so that 0 x-7) with a...
2. Consider a thin rod of length L = π (so that 0 x-7) with a general internal source of heat, Q(a,t) Ot (10) subject to insulated boundary conditions The initial temperature of the bar is zero a(x, 0) = 0 (12) (a) (3pts) What is k in (10)? (b) (10pts) Assume a separable solution to the homogeneous version of the PDE and boundary conditions (10)-(11) of the form u(r, t)- o(x)G(t). Write down or find the eigenvalues λη and...
Problem 1: We are interested in solving a modified form of diffusion equation given below using Fourier transforms au(x,t) The domain of the problem is-oo < x < oo and is 0 < t < oo . At...
Problem 1: We are interested in solving a modified form of diffusion equation given below using Fourier transforms au(x,t) The domain of the problem is-oo < x < oo and is 0 < t < oo . At time t = 0, the initial condition is given by u (x,0)-0 a) Take the Fourier transform on x and show that the above PDE can be transformed into the following ODE where G() is the Fourier transform of g(x) and U(w,...
Recall that the differential equation for the instantaneous charge q(t) on the capacitor in an RC-series circuit is dt C Use the Laplace transform to find the charge q(t) on the capacitor in an RC-series circuit subject to the given conditions q(0) = 0, R = 2.5 Ω, C = 0.08 , E(t) given in the figure below q(t) = E(t) 3 eBook
Please answer parts c-d only.
4. In lab 4 we consider the differential equation y" 2yywyF(t) for different forcing terms F(t). In this problem we analyze this equation further using Laplace transforms 0, t<1 (a) Consider y" + y, +40y-1(t), where I(t)- t < 2. Find 1 1, 0. t>2 the forward transform Y-E(y) if y(0)-y(0)-0 (b) Solve y" + y, + 40y-1, y(0) = y'(0) = 0, using Laplace transforms Notice how the value of Y (s) you obtain...
1. Solve the boundary value problem ut =-3uzzzz + 5uzz, u(z, 0) = r(z) (-00 < z < oo, t > 0), using direct and inverse Fourier transforms U(w,t)-홅启u(z, t) ei r dr, u(z,t)-二U( ,t) e ur d . You need to explain where you use linearity of Fourier transform and how you transform derivatives in z and in t 2. Find the Fourier transform F() of the following function f(x) and determine whether F() is a continuous function (a)...
If = Q, where Q is a function of y only, then the differential equation M + Ny = 0 has an integrating factor of the form +(y) = es Q(u) dy Find an integrating factor and solve the given equation. ydx + (3xy - e-39) dy=0 Enclose arguments of functions in parentheses. For example, sin (22) To enter y in text mode, type (ly) or abs(y). Use multiplication sign in all cases of multiplication. The integrating factor is (y)...
problem 1) Find the differential equation describing the
amount of salt,Qb, in the tank for times t in the interval t>=T.
Then solve to obtain Qb(t) for t>= T
A Water Tank Problem with Discontinuous Source A water tank contains V > 0 liters of pure water and Qo grams of salt. At time t = 0 we start pouring water into the tank with a rate r >0 liters per minute with a salt concentration of q> 0 grams...
y(t) is
INCORRECT
but
x(t) is CORRECT
DIFFERENTIAL EQUATIONS / Linear Algebra
Only people that are proficient in DIFFERENTIAL EQUATIONS should
even attempt to solve. No beginners or amateurs allowed.
Please write clearly and legibly. No sloppy Handwriting. I must
be able to clearly and easily read your solution and answer.
Circle final answer.
BELOW is an example of what the answer should look very similar
to. should be in the same form basically.
example
7.10.4 Question Help Use the...
I H C0 005 f Recall that the differential equation for the instantaneous charge g(0) on the capacitor in an series circuit is LRC 2 dq 1 Use the Laplace transform (show all work on separate paper) when L = 1h, R-20 Ω, C= 0.005 f, E(t) 140 V, i> 0, q(0) 0, and i(0) 0 to find a) q(t)- b) What is the current i(t)?
The position x of a mass m attached to a spring obeys the differential equation i + yi + w?x = 0 where y 2w. a) (2 marks) Write down expressions for the forces on the mass due to (i) the spring, and (ii) damping. (3 marks) Using a trial solution x = Ae"', show that a = --y/2 ± (y2/4 - «2)1/2 b) c) (4 marks) Show, by finding wd, that the solution is a damped oscillation of the...
2. Consider a thin rod of length L = π (so that 0 x-7) with a general internal source of heat, Q(a,t) Ot (10) subject to insulated boundary conditions The initial temperature of the bar is zero a(x, 0) = 0 (12) (a) (3pts) What is k in (10)? (b) (10pts) Assume a separable solution to the homogeneous version of the PDE and boundary conditions (10)-(11) of the form u(r, t)- o(x)G(t). Write down or find the eigenvalues λη and...
Problem 1: We are interested in solving a modified form of diffusion equation given below using Fourier transforms au(x,t) The domain of the problem is-oo < x < oo and is 0 < t < oo . At time t = 0, the initial condition is given by u (x,0)-0 a) Take the Fourier transform on x and show that the above PDE can be transformed into the following ODE where G() is the Fourier transform of g(x) and U(w,...
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