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- The mathematical models of some continuous time systems are given above. x(t) is the input signal of the system, and y(t) is the output signal of the system. Which of the following systems is linear and which is nonlinear? For linear systems, write "linear" in the space next to the option. For non-linear systems, write "non-linear" in the space next to the option.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.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.
- Given the plant transfer function, G(s) = 90/ s(s+4) and H(s) = 1. Obtain (i) characteristic equation (ii) damped frequency of oscillation (iii) damping ratio (iv) settling time (v) delay timeThe 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.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.
- 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? calculateGiven 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 solution15 - 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 for t = 0.2 s and c (infinity) = 0.333 for t = infinity. What is the steady-state error of the system? calculate.A) 0.33B) 0C) 0.25D) 0.5E) 0.67
- GIven the difference equation:y(n)=0.0899x(n)+0.0257x(n−1)−0.0257x(n−2)−0.0899x(n−3)+1.6148y(n−1)−1.9395y(n−2)+1.2807y(n−3)−0.5852y(n−4)Solve the following:1.) The system function, H(z)2.) Poles and zerosConsider 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 confirmedA forced excited m–k–c system is under a harmonic force F: F=5000sinωt If the mass m = 50 kg; k=80E3 N/m; damping ratio=0.3 and dynamic deflection is to be less than 0.08 m. Determine the range of operating excitation frequency. Also the show the operating range of frequency on a graph.