A system is modeled by the following LTI ODE: ä(t) +5.1640.j(t) + 106.6667x(t) = u(t) where...
(3) For the system modeled by with output defined as a) Find the system's transfer function(s) E(t) +3z(t) +2x(t)-Sult) b) Find the system's pole(s) (if any) and zero(s) (if any) c) Find n(t →x) if u(t)-G 120) 0 t<0 e) Find the frequency response function corresponding to output y 1) Find steady-state ya(t) if u(t) 3sin(21)
The output of an LTI system is yı(t) when xy(t) is the input. System yı(t) -1 1 The output of the system is yz(t) when x2(t) is the input. x (t) 3 N yz(t) System Express yz(t) in terms of yı(t) using the following format yz(t) = a, y(t-by) + a2 yı(t-b2)
Problem 5: A measurement system can be modeled by using the following second-order ODE: j(t)2)4y(t)= 8U (t) - (a) Determine the natural frequency, damping ratio, and sensitivity of the system. (b) If the system is used to measure a harmonic signal U(t) 5sin(5t), calculate the magnitude ratio and phase shift (c) What is the range of the signal frequencies that this device can measure so that the resulting dynamic error is within ± 20 %? Problem 5: A measurement system...
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)...
1. An LTI system has the transfer function (or frequency response) H(u)- a) What is the magnitude of H()? b) What is the phase of H(u)? c) Determine the impulse response of this system. d) Find the differential equation between the input and output of this system. e) What is the output of the system to the input x()c
14. An LTI system has the following transfer function, determine the output system response y(t) due to the input x(t) e u(t) H(s) s+2 S+7s+12 Answer: y(t)
Consider an LTI system with the impulse response h(t) = e- . Is the system casual? Explain. Find and plot the output s(t) given that the system input is x(t) = u(t). Note that s(t) in this case is commonly known as the step response of the system. If the input is x(t) = u(t)-u(t-T). Express the output y(t) as a function of s(t). Also, explicitly write the output y(t) as a function of t. a) b) c)
Use Laplace transformations to solve the following ODE for (t): ä(t) + 2r(t) = u(t) + 3u(t) Assume: u(t) = e- and initial conditions 2(0) = 1, +(0) = 0, u(0) = 0,
Given a zero-state LTI system whose impulse response h(t) = u(t) u(t-2), if the input of the system is r(t), find the system equation which relates the input to the output y(t) 4. (20 points) If a causal signal's s-domain representation is given as X (s) = (s+ 2)(s2 +2s + 5) (a) find all the poles and zero of the function. 2 1 52243 orr
A CT LTI system with impulse response h(t) = u(t)−u(t−1) is given the input x(t) = (1 − |t|)(u(t + 1) − u(t − 1)). Find the output of the system.