Homework Answers
Add Answer to:
Problem l: (13 pts) mper system subject to a constant force is described by the following...
damped forced mass-spring system with m 2, and k 26, under the 2 Consider a influence...
damped forced mass-spring system with m 2, and k 26, under the 2 Consider a influence of an external force F(t)= 82 cos (4t) 1, 7 = a) (8 points) Find the position u(t) of the mass at any time t, if u(0) 6 and u'(0) = 0. b) (4 points) Find the transient solution u(t) and the steady state solution U(t). How would you characterize these two solutions in terms of their behavior in time? We were unable to...
Partial Differential Equations : 8+1 pts) the following Heat problem or (o,)-1, (1-2 0 e steady state solution y(x). e transient solution ω(x,t) using the corresponding homogenous Heat proble ll...
Partial Differential Equations : 8+1 pts) the following Heat problem or (o,)-1, (1-2 0 e steady state solution y(x). e transient solution ω(x,t) using the corresponding homogenous Heat proble ll the steps). e complete solution of (1).
Partial Differential Equations : 8+1 pts) the following Heat problem or (o,)-1, (1-2 0 e steady state solution y(x). e transient solution ω(x,t) using the corresponding homogenous Heat proble ll the steps). e complete solution of (1).
Consider a damped forced mass-spring system with m = 1, γ = 2, and k =...
Consider a damped forced mass-spring system with m = 1, γ = 2, and k = 26, under the influence of an external force F(t) = 82 cos(4t). a) (8 points) Find the position u(t) of the mass at any time t, if u(0) = 6 and u 0 (0) = 0. b) (4 points) Find the transient solution uc(t) and the steady state solution U(t). How would you characterize these two solutions in terms of their behavior in time?...
Consider the diffusion problem au Ou u(0, t) = 0, u(L, t) = 50 u(x,0-fx where FER is a constant, ...
Mark which statements below are true, using the following:
Consider the diffusion problem au Ou u(0, t) = 0, u(L, t) = 50 u(x,0-fx where FER is a constant, forcing term. Any attempt to solve this using separation of variables fails. This is because the PDE is not homogeneous. A more fruitful approach arises from splitting the solution into the sum of two parts, taking into account that all change eventually dies out. That is there is a transient part...
(5) For the system described by the following difference equation y(n)= 0.9051y(n 1) 0.598y(n 2) -0.29y(n...
(5) For the system described by the following difference equation y(n)= 0.9051y(n 1) 0.598y(n 2) -0.29y(n 3) 0.1958y(n - 4) +0.207r(n)0.413r(n 2)+0.207a(n - 4) (a) Plot the magnitude and phase responses of the above system. What is the type of this filter? (b) (b) Find and plot the response of the system to the input signal given by /6)sin(w2n +T /4) u(n), where w 0.25m and ws 0.45m a(n) 4cos(win -T = (c) Determine the steady-state output and hence find...
Problem 3. Consider the following continuous differential equation dx dt = αx − 2xy dy dt...
Problem 3. Consider the following continuous differential equation dx dt = αx − 2xy dy dt = 3xy − y 3a (5 pts): Find the steady states of the system. 3b (15 pts): Linearize the model about each of the fixed points and determine the type of stability. 3b (15 pts): Draw the phase portrait for this system, including nullclines, flow trajectories, and all fixed points. Problem 2 (25 pts): Two-dimensional linear ODEs For the following linear systems, identify the...
3) Consider the following vibrating system u" (1/4) 2u 2 cos (wt), u (0) 0, (0) 2 (a) Find transient and steady states of solution (b) Find the amplitude R of the steady state solution in terms o...
3) Consider the following vibrating system u" (1/4) 2u 2 cos (wt), u (0) 0, (0) 2 (a) Find transient and steady states of solution (b) Find the amplitude R of the steady state solution in terms of w and plot R versus w; (c) Find Rmax and wmax
3) Consider the following vibrating system u" (1/4) 2u 2 cos (wt), u (0) 0, (0) 2 (a) Find transient and steady states of solution (b) Find the amplitude R of...
Problem 4: (65 points) Let a system be given by the state space representation 8 8...
Problem 4: (65 points) Let a system be given by the state space representation 8 8 10 * = X+ u(t), y = [1 -1]x – u(t) 1 1 -1 0 Y(S) d) (7) Find the transfer function US) e) (5) Is the system BIBO stable? 3 f) (9) Let the initial state x(0) -3 u(t) = 0) for all t > 0. = Find the zero input response (i.e., with the input
(1 point) For partial derivatives of a function use the subscript notation, so for the second par...
(1 point) For partial derivatives of a function use the subscript notation, so for the second partial derivative of the function u(x,t) with respect to x use uxx. For ordinary differential equations use the prime notation, so the second derivative of the function f(x) is f" Solve the heat equation 14 1502,>0 a(0,t) = 92,21(2, t) 87, t > 0 using a steady-state and transient solution: ie write u(z, 1) _ u(z,t) + S(z) with u a solution of the...
7. Answer the questions below for the following initial value problem: y (t) = sin y,...
7. Answer the questions below for the following initial value problem: y (t) = sin y, 0 <y(0) < 27. (a) [1 pt) Determine the equilibrium (i.e., critical or steady-state) solutions. (b) (2 pts) Construct a sign chart for y' = sin y. Hy' = sin y 21 (c) (3 pts] Now construct a sign chart for y", and find the inflection points (if any). Hy" = f(y) 271 (d) [5 pts] Draw the phase line, and sketch a graph...
damped forced mass-spring system with m 2, and k 26, under the 2 Consider a influence of an external force F(t)= 82 cos (4t) 1, 7 = a) (8 points) Find the position u(t) of the mass at any time t, if u(0) 6 and u'(0) = 0. b) (4 points) Find the transient solution u(t) and the steady state solution U(t). How would you characterize these two solutions in terms of their behavior in time? We were unable to...
Partial Differential Equations : 8+1 pts) the following Heat problem or (o,)-1, (1-2 0 e steady state solution y(x). e transient solution ω(x,t) using the corresponding homogenous Heat proble ll the steps). e complete solution of (1).
Partial Differential Equations : 8+1 pts) the following Heat problem or (o,)-1, (1-2 0 e steady state solution y(x). e transient solution ω(x,t) using the corresponding homogenous Heat proble ll the steps). e complete solution of (1).
Mark which statements below are true, using the following:
Consider the diffusion problem au Ou u(0, t) = 0, u(L, t) = 50 u(x,0-fx where FER is a constant, forcing term. Any attempt to solve this using separation of variables fails. This is because the PDE is not homogeneous. A more fruitful approach arises from splitting the solution into the sum of two parts, taking into account that all change eventually dies out. That is there is a transient part...
(5) For the system described by the following difference equation y(n)= 0.9051y(n 1) 0.598y(n 2) -0.29y(n 3) 0.1958y(n - 4) +0.207r(n)0.413r(n 2)+0.207a(n - 4) (a) Plot the magnitude and phase responses of the above system. What is the type of this filter? (b) (b) Find and plot the response of the system to the input signal given by /6)sin(w2n +T /4) u(n), where w 0.25m and ws 0.45m a(n) 4cos(win -T = (c) Determine the steady-state output and hence find...
3) Consider the following vibrating system u" (1/4) 2u 2 cos (wt), u (0) 0, (0) 2 (a) Find transient and steady states of solution (b) Find the amplitude R of the steady state solution in terms of w and plot R versus w; (c) Find Rmax and wmax
3) Consider the following vibrating system u" (1/4) 2u 2 cos (wt), u (0) 0, (0) 2 (a) Find transient and steady states of solution (b) Find the amplitude R of...
Problem 4: (65 points) Let a system be given by the state space representation 8 8 10 * = X+ u(t), y = [1 -1]x – u(t) 1 1 -1 0 Y(S) d) (7) Find the transfer function US) e) (5) Is the system BIBO stable? 3 f) (9) Let the initial state x(0) -3 u(t) = 0) for all t > 0. = Find the zero input response (i.e., with the input
(1 point) For partial derivatives of a function use the subscript notation, so for the second partial derivative of the function u(x,t) with respect to x use uxx. For ordinary differential equations use the prime notation, so the second derivative of the function f(x) is f" Solve the heat equation 14 1502,>0 a(0,t) = 92,21(2, t) 87, t > 0 using a steady-state and transient solution: ie write u(z, 1) _ u(z,t) + S(z) with u a solution of the...
7. Answer the questions below for the following initial value problem: y (t) = sin y, 0 <y(0) < 27. (a) [1 pt) Determine the equilibrium (i.e., critical or steady-state) solutions. (b) (2 pts) Construct a sign chart for y' = sin y. Hy' = sin y 21 (c) (3 pts] Now construct a sign chart for y", and find the inflection points (if any). Hy" = f(y) 271 (d) [5 pts] Draw the phase line, and sketch a graph...
Most questions answered within 3 hours.
-
Where is the error in this code sequence?
String s1 = "Hello";
String s2 = "ello";...
asked 10 months ago -
Financial data for Joel de Paris, Inc., for last year
follow:
Joel de Paris, Inc.
Balance...
asked 10 months ago -
Consider this reaction:
Al2(SO4)3 (aq)+ BaCl3
(aq) Al2Cl6 (aq)- +
3BaSO4(s) . What is the...
asked 10 months ago -
Suppose that Savneet is considering increasing her
recent random sample from 20 car rentals to 40...
asked 10 months ago -
Trucks arrive at an unloading terminal at an average rate of 120
per hour.
Trucks arrive...
asked 10 months ago -
Why are methanol and ethanol completely soluble in water while
octanol is not very little soluble....
asked 10 months ago -
A facilities manager at a university reads in a research report
that the mean amount of...
asked 10 months ago -
When the CuSO4 is rehydrated by adding water to the anhydrous
compound, is this an endothermic...
asked 10 months ago -
A ray of sunlight is passing from diamond into crown glass; the
angle of incidence is...
asked 10 months ago -
A block of mass 0.249 kg is placed on top of a light, vertical
spring of...
asked 10 months ago -
how do the kidneys compensate in the presences of acidosis
a) trigger hyperventilate
b) reserve acid...
asked 10 months ago -
Question 501 pts
The rental rate of capital to the firm increases. Which of the
following...
asked 10 months ago