For the circuit shown in figure below, find the differential equation relating output y(t) to the input x(t). y(t) 0.25 H x(t) 0.25 N 2 F
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- When the unit step function is applied to the input of the system whose block diagram is given below, the output response takes the value c (0.2) = 0.11 for t = 0.2 s and c (infinity) = 0.333 for t = infinity. What is the steady-state error of the system? calculate.Consider a system whose input x (t) and output y (t) satisfy the differential equation of the first order dy(t)/dt + 2y(t) = x(t) The system also satisfies the initial rest condition. Determine the output of the system y (t) when the input is x (t) = e ^3t u(t)Determine the validity of the second-order approximation for the function. Justify your answer. G(S) = 1/(s + 4)(S2 + 4S + 8)
- For a DA converter, the LRC circuit chosen has inductance L= 10 H , resistance R= 10 ohms and inductance C= 0.2 F . The input digital signal is a power surge (impulse) of magnitude 100 V lasting an instant at t = a . Use your notes to model the second order differential equation in terms of the charge q suited to this application. Simplify the equation with the coefficient of q'' as 1. Use the Laplace transform and calculate the (general) output voltage vo if vo = 1/C q . Your solution will be in terms of a . Use the initial conditions q(0)=0 and q'(0)=0 . Do not use Matlab as its solution will not be identifiable in the solution entry. You must indicate in your solution:1. The simplified differential equation in terms of the charge q you will be solving2. The simplified Laplace transform of this equation where you have made L{q} subject of the equation3. The partial fractions process if required4. The completing the square process if required5. Express the solution q as a piecewise…Take the system with the input x, and output y, and the input-outputrelationshipy(n) = 0.75y(n − 1) + 0.2x(n) Find the step response. What is the steady state value of the response y(∞)?When the unit step function is applied to the system input given the block diagram below, the output response takes the value c (0.2) = 0.11 fort = 0.2 s and c (infinity) = 0.333 for t = infinity. What is the steady-state error of the system? calculate
- Find the time-domain expression(A) ? = 18.6 ∠ − 54° ?(B) ? = (20 ∠45° - 50 ∠ − 30° ) mA(C) ? = (20 + ?80 − 30 ∠15° ) �a) Y(ω) = 1/(5+jω) The expression above defines the frequency domain signal Y(ω) from a time domain signal y(t) i) Determine the imaginary & real parts of Y(ω). ii.Determine the signal y(t) that produced the signal Y(ω). b)What are the 3 areas of application of i.Signals ii.Systems c) Briefly summarise with explanation the difference between discrete & continuous time signal and also write an expression that describes each signal type.f(x3, x2, x1, x0) = ∑m(4,8,10,11,12,15) Draw the circuit to implement by minimizing the function with the Quine McCluskey method.
- A discrete time signal x(n)=[1,2,3,4] for n=0 to 3 is provided. What will be the time domain representation of the signal x(n/2)?The two signals are expressed as: X(t) =Xe(t) + XO(t). a. Derive the function of Xe(t) in continuous time for both even and odd signals respectively. b. With the given X(n), kindly derive an expression for the Discrete Time for both even and odd signals assuming that this function holds X(n) = Xe (n) + XO(n).A discrete time signal is given by: x(n) = [2, 2, 2, 2, 3] Sketch the following signals : x(n) u(n-1)