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2. For this differential equation y"(t) - 6y'(t) + 15y(t) = 2r(t), determine (4 points) a)...
Question 2 (15 points) Solve the differential equation for the general solution y 6y' 73y 0 y(t) C cos(3t) C2 sin(3t) y(t) = C1 cos(8t) + C2 sin(8t) y(t) cos(8t) +C2e" sin(St) y(t) Ce cos(8t) Cest sin (8t) y (t) = Cleft cos (8t) + C2eft sin (8t) (t)Cest cos(9)Cesin (9t) Previous Page Next Page Page 2 of9
2. for the following differential equation: y + 8y + 15y-u 30u, y(0)-1,y(0) 0,u(t)-t fort20 3. Find the transfer function
Problem#3 (16 points) Consider a system that has R(S) as the input and Y (S) as the output. The transfer function is given by: Y(S) R(S) 45+12 What are the poles of the system? For r(t) output in the time-domain y(t) For r(t) = t, t output in the time-domain y(t) 1- 2- 1,t 0, use partial fraction expansion and inverse Laplace transform to find the 3- 0, use partial fraction expansion and inverse Laplace transform to find the
Given h(t)=(e-t+e-3t)u(t) find: A) The transfer function H(s). B) The locations of all poles and zeros. C) Determine if the system is stable or not D) Find the differential equation for this system.
Find the general solution of the given differential equation. y" - 6y' + 6y = Here y(t) =
USING MATLAB Please post code 1. Solve the 2nd order differential equation ?+89 +15y-sin(t), y(0)-1,?(0)-2 symbolically and numerically, and plot both results together over the time interval 0,10 sec. Provide appropriate labels on both axes, a title, and a legend that denotes each solution. Check your symbolic answer by using the Matlab DIFF function to compute the appropriate derivatives and then substituting them into the differential equation.
Given the following system, where Gs(s) - -e2) Given the following system, where Gc(s) S+3 3s++2) and H(s)s R(S) . Gc(s) G(s) Y(s) SOLVE IN MATLAB CODE ONLY Obtain the transfer function of the system above. Find zeros, poles, and gain of the transfer function and plot zeros and poles. Rewrite the transfer function using the partial fraction expansion. Graph the Step response. Graph the impulse response.
4. Consider the differential equation y' - 6y' + 9y = 4e3t a) Find the general solution of the differential equation. b) Solve the IVP: Y" - 6y' +9y = 4e3with y(0) = 1 and y'(0) = 10.
Problem 1 (20 points) Consider the differential equation for the function y given by 4 cos(4y) 40e 2e) cos(8t)+5 eu 2t) sin(8t)/ - 12e - 0. 8 sin(4y) y a. (4/20) Just by reordering terms on the left hand side above, write the equation as Ny + M 0 for appropriate functions N, M. Then compute: aN(t, y) ayM(t, y) b. (8/20) Find an integrating factor If you keep an integrating constant, call it c (t) N and M M,...
2.6.1-2.6.62.6.1 Consider a causal contimuous-time LTI system described by the differential equation$$ y^{\prime \prime}(t)+y(t)=x(t) $$(a) Find the transfer function \(H(s)\), its \(R O C\), and its poles.(b) Find the impulse response \(h(t)\).(c) Classify the system as stable/unstable.(d) Find the step response of the system.2.6.2 Given the impulse response of a continuous-time LTI system, find the transfer function \(H(s),\) the \(\mathrm{ROC}\) of \(H(s)\), and the poles of the system. Also find the differential equation describing each system.(a) \(h(t)=\sin (3 t) u(t)\)(b)...