3. Classify the following linear differential equations according to whether they are time-variable or time-invariant. Indicate the time-variable term/s if it is time-variable. A. d²y d1² |+2y=0 d −(1²y) = 0 d²y + t +1 di² 1+ + (cost) y = 0 B. C. D. d²y dt²
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- A)Perform the N=5 point circular convolution of x and h using DFT. B)Perform the N=5 point circular convolution of x and h in time-domain.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? calculateWhen 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.
- Using the DIFFERENTIAL EQUATION METHODS, Solve for the particular solution of the differential equation as follows:y"'+ 33y"+ 30y'− 64y= 0With the initial conditions as follows: y(0) = 0, y’(0) = -1, y’’’(0) = 33.Consider the circuit on the left. DC voltage u1(t ≥ 0) = U is applied at time t = 0. Both meshes must include the input voltage. At time t = 0, the capacitors are free of energy. The following applies: τ = R*C. Derive the 2nd order differential equation for the capacitor voltage u2(t).Given the ff. second-order differential equation: y[n] + 1.4y[n-1] + 0.45y[n-2] = x[n] - x[n-1] with an input of x[n] = 0.1nu[n] and initial conditions y[-1] = 0 and y[-2] = 1. Find the following: 1. Characteristic equation and its roots. 2. Form of the homogeneous solution 3. Particular solution
- Signal and system The mathematical model of a system is y" (t) + ay'(t) + by(t) = a (t) + ca (t) where a=1, b=2 and c=1. 1) Find zeros and poles of the system. 2) Show them onto the S-Plane (the complex plane) 3) Discuss the BIBO stability of the system.The response of a system, h(t) is given as in Figure 1 below where the amplitudeof this signal is 7. Then,this system is excited by an input of x(t) = (u(t) × (u(-t)+u(t))) /1. 1)Illustrate the input signal, x(t). 2)Calculate the convolution output of the system y(t) = x(t) ∗ h(t). Nextdetermine y(t) when t is 1 sec 2)Prove the solution in Q2 is comparable when solving in frequency domain(Laplace). Next, sketch the signal for convolution output.Consider two systems one is second order and the other is third order. The characteristic equations are: as2+bs+c for the second order and as3+bs2+cs+d for the third order, where a,b,c,d are positive real numbers. Then which of the following is correct with regard to the stability of these two systems? a. stability of either system cannot be confirmed with the given data b. third order is definitely stable but second order cannot be confirmed c. both systems are definitely stable d. second order is definitely stable but third order cannot be confirmed
- Q: In the network of Fig. (1), the switch is closed at t=0 and there is no initial charge on either of the capacitors. Find the resulting current ( i ). (Using Laplace Transform). 100 Fig. 1The characteristic equation of a system is given by S5+2S4+S3+2S2+S+5=0 Determine (i) Stability of the system (ii) Number of roots on the right side of 's' - Plane (iii) Number of roots on the left side of 's' - PlaneI need help with the question below Consider a causal LTI continuous system described by the differential equation y′′(t) + 3y′(t) + 2y(t) = x(t) where y(t) is the system output and x(t) is the input.1. Find the transfer function H(s) of the system.2. Find its poles and zeros. From its poles and zeros, determine if the system is BIBO stable or not.3. If x(t) = u(t) and initial conditions are zero, determine the steady-state response yss(t)4. If the initial conditions were not zero, would you get the same steady state?. Explain