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 |+ 2y = 0 di B. C. D. d (1²y) = 0 dt d²y (+1)+(+1) = 0 d²y dt² + (cost) y = 0
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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.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 confirmedThe characteristic equation of a system is given as s3+25s2+10s+50=0. What is the number of the roots in the right half s-plane and the imaginary axis respectively?
- 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.The 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' - PlaneStates Gauess's law and obtain both integral and differential form of 1st Maxwell's equation. You must mathematically prove it.(no chat gpt only handwritten otherwise downvote)
- Obtain the value of I1, if ? =1/√2 ?, and the circuit is in steady state at t = 0Suppose an electrical signal generated, y(t) can be modelled as follows where t, is time in second, y(t) is voltage in mv. a) Produce graphs showing the amplitude and phase spectrum of y(t). b) State whether this time-domain signal y(t) is periodical, or non-periodical and justify your answer.1. An electromotive force ?(?)={0 volts,0≤?<1. 2 volts,?≥1 is applied to an RC-series circuit in which the resistance is 10 ohms and the capacitance is 0.32 farad. If the initial charge ?(0)=0,(a) Specify the differential equation as an IVP for the RC-series circuit.(b) Apply Laplace Transform to solve the IVP and find the charge ?(?) at any time t.
- 5. If an electric circuit LRC in series, contains an inductor, a resistor and a capacitor, the differential equation for the instantaneous charge q(t) of the capacitor is given by: ******* Equation ****** Use the Laplace transform to determine q(t) if L =(1/4) Hertz. R= 3 ohms, C =(1/9) farads and E(t) = 120 volts, t>0, q(0)=0, i(0)=0. Could you please help me with this?A system has the following characteristic equation: s + s + 3 + 2s + 2 = 0 Using the Routh-Hurwitz method, checkConsider 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).