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Manufactiring System Dynamics
1. Given: S +3 Find f(t)? (40 points) 2. IF f(t) t Prove...
3. (25 Points) Find f(t). f(0) + f(t - 1)f(t)dt = t. Hint: The second term...
3. (25 Points) Find f(t). f(0) + f(t - 1)f(t)dt = t. Hint: The second term on the left side is a convolution and it might be helpful to use the Laplace Transform. 1 4. (10 Points) Solve the initial value problem by Laplace transform techniques. x" + 5x' + 4x = 0;x(0) = 1,x'(0) = 0. I 5. (15 Points) Find a series solution for the following differential equation. Calculate the radius of convergence. 2(x - 1)y' = 3y...
Problem 1: Find the Laplace transform X(s) of x(0)-6cos(Sr-3)u(t-3). 10 Problem 2: (a) Find the inverse...
Problem 1: Find the Laplace transform X(s) of x(0)-6cos(Sr-3)u(t-3). 10 Problem 2: (a) Find the inverse Laplace transform h() of H(s)-10s+34 (Hint: use the Laplace transform pair for Decaying Sine or Generic Oscillatory Decay.) (b) Draw the corresponding direct form II block diagram of the system described by H(s) and (c) determine the corresponding differential equation. Problem 3: Using the unilateral Laplace transform, solve the following differential equation with the given initial condition: y)+5y(0) 2u), y(0)1 Problem 4: For the...
2. a) Find the solutions (t) and y(t) of the system of differential equations: 10y, y10 by converting the system into a...
2. a) Find the solutions (t) and y(t) of the system of differential equations: 10y, y10 by converting the system into a single second order differential equation, then solve it. The initial conditions are given by r(0) 3 and y(0)-4. Show your full work. [7 marks] b) For t = [0, 2n/5]: identify the parametric curve r(t) (t),(t)), find its cartesian equation, then sketch it. Hint: You can use parametric plots in Matlab or just sketch the curve by hand....
Solve question 2. Question 1 posted below for reference 2. a. If f(t) in the previous...
Solve question 2. Question 1 posted below for reference
2. a. If f(t) in the previous question was replaced by an impulse function at t2. Can you re-write the differential equation in the last problem? b. Determine the response to the force impulse at t=2 s. 1. a Can you write the function given in figure 1 as a Fourier series? Why? Af(t) 1 2 3 4 5 6 7 Figure 1 b. If your answer to the previous question...
[-/2 Points] DETAILS Find the general solution of the given system. 4 - 1 2 X'...
[-/2 Points] DETAILS Find the general solution of the given system. 4 - 1 2 X' = -1 4 0 X -1 04 X(t) = Submit Answer [-/2 Points] DETAILS Solve the given initial-value problem. (1 -4 -6 X' = 1 2-3 X, X(0) = 1 -2 - 2 X(t) [-/2 points) DETAILS Solve the given initial-value problem. X' = 8 -1 5 +6)x, x(0) = (-3) X(t)
The dynamics of a spring-damper-mass system is defined by the following differential equation, č + 4€...
The dynamics of a spring-damper-mass system is defined by the following differential equation, č + 4€ + 5x = f(t),x(0) = 1, *(0) = 2, where f(t) is a step input with magnitude of 10, i.e. f(t)=10-1(t). Find the solution x(t) of the differential equation using Laplace transformation method.
2. [-/3 Points] DETAILS ZILLENGMATH6 13.3.002. du at 0<x<L, t> 0 subject to the given conditions....
2. [-/3 Points] DETAILS ZILLENGMATH6 13.3.002. du at 0<x<L, t> 0 subject to the given conditions. Assume a rod of length L. Solve the heat equation Lazu axz u(0, 1) = 0, u(L, t) = 0 u(x,0) = x(L - x) u(x, t) = + n = 1 eBook
(1) (2) (3) 5. (20 points) a) Solve the following system of equation for symbolic 2,...
(1) (2) (3) 5. (20 points) a) Solve the following system of equation for symbolic 2, 4, 2 3x - 2y +52 = 12 2-32 + y = -1 2-y-* = 4 b) State the code for solving the following ordinary differential equation 204 - 3y = t?, y(0) = 0,//(0) = 1. ata c) Plot the following symbolic functions a) f(x) = for symbolic r in (-2,2) interval. b) f(x,y) = sin(x2+x2) in (-5,5). - 2 at (4)
problem 7 Problem-4 [10 Points] Find the Laplace transforms of the functions in Figure. 2 Figure....
problem 7
Problem-4 [10 Points] Find the Laplace transforms of the functions in Figure. 2 Figure. 2: Triangular Function Problem-5 [10 Pointsl A system has the transfer function h(s) = (s1)(s +2) a) Find the impulse response of the system b) Determine the output y(t), given that the input is x(t) u(t) Problem-6 [10 Pointsl Use the Laplace transform to solve the differential equation +22+10v(t) 3 cos(2t) dt2 dt subject to v(0)-1, dv(O) Problem-7 [10 Points] Solve the integrodifferential equation...
a) (3 points) Find the general solution to the equation. Use C, G.C.. to denote arbitrary...
a) (3 points) Find the general solution to the equation. Use C, G.C.. to denote arbitrary constants as necessary y"(.) - 45e + sint b) (5 points) Solve the following separable differential equation for the given initial condition In (1) 0 c) (5 points) Solve the following first-order linear differential equation for the given initial condition y' .9 -3, y(0- 1 c) (5 points) Solve the following first-order linear differential equation for the given initial condition. y'(t) + 9 =...
3. (25 Points) Find f(t). f(0) + f(t - 1)f(t)dt = t. Hint: The second term on the left side is a convolution and it might be helpful to use the Laplace Transform. 1 4. (10 Points) Solve the initial value problem by Laplace transform techniques. x" + 5x' + 4x = 0;x(0) = 1,x'(0) = 0. I 5. (15 Points) Find a series solution for the following differential equation. Calculate the radius of convergence. 2(x - 1)y' = 3y...
Problem 1: Find the Laplace transform X(s) of x(0)-6cos(Sr-3)u(t-3). 10 Problem 2: (a) Find the inverse Laplace transform h() of H(s)-10s+34 (Hint: use the Laplace transform pair for Decaying Sine or Generic Oscillatory Decay.) (b) Draw the corresponding direct form II block diagram of the system described by H(s) and (c) determine the corresponding differential equation. Problem 3: Using the unilateral Laplace transform, solve the following differential equation with the given initial condition: y)+5y(0) 2u), y(0)1 Problem 4: For the...
2. a) Find the solutions (t) and y(t) of the system of differential equations: 10y, y10 by converting the system into a single second order differential equation, then solve it. The initial conditions are given by r(0) 3 and y(0)-4. Show your full work. [7 marks] b) For t = [0, 2n/5]: identify the parametric curve r(t) (t),(t)), find its cartesian equation, then sketch it. Hint: You can use parametric plots in Matlab or just sketch the curve by hand....
Solve question 2. Question 1 posted below for reference
2. a. If f(t) in the previous question was replaced by an impulse function at t2. Can you re-write the differential equation in the last problem? b. Determine the response to the force impulse at t=2 s. 1. a Can you write the function given in figure 1 as a Fourier series? Why? Af(t) 1 2 3 4 5 6 7 Figure 1 b. If your answer to the previous question...
[-/2 Points] DETAILS Find the general solution of the given system. 4 - 1 2 X' = -1 4 0 X -1 04 X(t) = Submit Answer [-/2 Points] DETAILS Solve the given initial-value problem. (1 -4 -6 X' = 1 2-3 X, X(0) = 1 -2 - 2 X(t) [-/2 points) DETAILS Solve the given initial-value problem. X' = 8 -1 5 +6)x, x(0) = (-3) X(t)
The dynamics of a spring-damper-mass system is defined by the following differential equation, č + 4€ + 5x = f(t),x(0) = 1, *(0) = 2, where f(t) is a step input with magnitude of 10, i.e. f(t)=10-1(t). Find the solution x(t) of the differential equation using Laplace transformation method.
2. [-/3 Points] DETAILS ZILLENGMATH6 13.3.002. du at 0<x<L, t> 0 subject to the given conditions. Assume a rod of length L. Solve the heat equation Lazu axz u(0, 1) = 0, u(L, t) = 0 u(x,0) = x(L - x) u(x, t) = + n = 1 eBook
(1) (2) (3) 5. (20 points) a) Solve the following system of equation for symbolic 2, 4, 2 3x - 2y +52 = 12 2-32 + y = -1 2-y-* = 4 b) State the code for solving the following ordinary differential equation 204 - 3y = t?, y(0) = 0,//(0) = 1. ata c) Plot the following symbolic functions a) f(x) = for symbolic r in (-2,2) interval. b) f(x,y) = sin(x2+x2) in (-5,5). - 2 at (4)
problem 7
Problem-4 [10 Points] Find the Laplace transforms of the functions in Figure. 2 Figure. 2: Triangular Function Problem-5 [10 Pointsl A system has the transfer function h(s) = (s1)(s +2) a) Find the impulse response of the system b) Determine the output y(t), given that the input is x(t) u(t) Problem-6 [10 Pointsl Use the Laplace transform to solve the differential equation +22+10v(t) 3 cos(2t) dt2 dt subject to v(0)-1, dv(O) Problem-7 [10 Points] Solve the integrodifferential equation...
a) (3 points) Find the general solution to the equation. Use C, G.C.. to denote arbitrary constants as necessary y"(.) - 45e + sint b) (5 points) Solve the following separable differential equation for the given initial condition In (1) 0 c) (5 points) Solve the following first-order linear differential equation for the given initial condition y' .9 -3, y(0- 1 c) (5 points) Solve the following first-order linear differential equation for the given initial condition. y'(t) + 9 =...
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