Q3. Let Grepresent a system described by the following differential equation: diye) + y(t) = dre)...
Let a linear system with input x(t) and output y(t) be described by the differential equation . (a) Compute the simplest math function form of the impulse response h(t) for this system. HINT: Remember that with zero initial conditions, the following Laplace transform pairs hold: Let the time-domain function p(t) be given by p(t) = g(3 − 0.5 t). (a) Compute the simplest piecewise math form for p(t). (b) Plot p(t) over the range 0 ≤ t ≤ 10 ....
Problem 1 (25 points): Consider a system described by the differential equation: +0)-at)y(t) = 3ú(1); where y) is the system output, u) is the system input, and a(t)is a function of time t. o) (10 points): Is the system linear? Why? P(15 points): Ifa(t) 2, find the state space equations?
An LT-I system with the following differential equation y’(t) + 3 y(t) = x(t) has a Zero State Response of yzsr(t) = -2 exp(-5t) u(t) + 2 exp(-3t) u(t) when an input signal: x(t) = 4 exp(-5t) u(t) is applied to the system. What is the Zero State Response of the following system beginning at time t = 0 seconds, y’(t) + 3 y(t) = x’(t) -2 x(t) if the same input signal is applied to the system, and it...
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)...
Question given an LTI system, characterized by the differential equation d’y() + 3 dy + 2y(t) = dr where x(t) is the input, and y(t) is the output of the system. a. Using the Fourier transform properties find the Frequency response of the system Hw). [3 Marks] b. Using the Fourier transform and assuming initial rest conditions, find the output y(t) for the input x(t) = e-u(t). [4 Marks] Bonus Question 3 Marks A given linear time invariant system turns...
Matlab code for the following problems. Consider the differential equation y(t) + 69(r) + 5y( Q3. t)u(t), where y(0) (0)0 and iu(t) is a unit step. Deter- mine the solution y(t) analytically and verify by co-plotting the analytic solution and the step response obtained with the step function. Consider the mechanical system depicted in Figure 4. The input is given by f(t), and the output is y(t). Determine the transfer function from f(t) to y(t) and, using an m-file, plot...
An LTI system is described by the following differential equation. Find the output when x(t)- u(t) and has the following initial conditions: y(0)= 1, (0) = 2 , and x(0)--I dy x dx +at + 4 y(t) = dt + x(t) Solution
1. A Consider the following nonhomogeneous differential equation: j(t) + (a - b)y(t) - aby(t) = x(t). Assume a and b are both strictly positive. The answers to nearly all of the questions below will be in terms of a and b. (a) (5 points) Is this system internally stable or unstable? Why? (b) (10 points) For arbitrary inital conditions yo and yo, write the zero-input response (ZIR) for t > 0. (c) (10 points) Derive this system's impulse response...
Please show all the steps, Thank you! Find yol(t), the zero-input component of the response for an LTIC system described by the following differential equation: (D2 + 6D +9)y(t) (3D+5)r(t) where the initial conditions are yo(0)-3)0(0) -7 Find yol(t), the zero-input component of the response for an LTIC system described by the following differential equation: (D2 + 6D +9)y(t) (3D+5)r(t) where the initial conditions are yo(0)-3)0(0) -7
Find the solution y of the initial value problem 3"(t) = 2 (3(t). y(1) = 0, y' (1) = 1. +3 g(t) = M Solve the initial value problem g(t) g” (t) + 50g (+)? = 0, y(0) = 1, y'(0) = 7. g(t) = Σ Use the reduction order method to find a second solution ya to the differential equation ty" + 12ty' +28 y = 0. knowing that the function yı(t) = + 4 is solution to that...