A) Find the differential equation of the circuit B). Obtain the transfer function H(s) of the circuit C. Obtain the impulse response h(t) of the system x(1) 4 R₁ R₂ y (1)

Consider the given signal æ (t) and the impulse response function h (t) . Find y(t) = x(t) * h(t) by evaluating the convolution integrals. Convolution properties cannot be applied here. f3 1sts3 to otherise 12 0sts1 h(t) = to otherise x(t) =

Reduce the function block diagram given below to find the transfer function for the system.  a. What is the unit impulse response of this system in the time domain? b. What is its unit step response?

A closed-loop transfer function is given as Calculate the response in the time domain y(t) for a unit step input.

please solve this with clear writing

Question #1 • Transfer function of an LTI continuous time system is given in the following form s+3 H(s) (s + 1)²(s² + 5s + 6) Obtain the impulse response of this system if it is a causal system. Obtain the impulse response of this system if it is a noncausal system. Obtain the impulse response of this system if it is an anticausal system. Sketch the pole-zero plot of the system for case (a) and give the differential equation that is used a) to express the input output relationship of this system.

Find the transfer function of the following circuit where R₁=R2=10002 and C=100μ x(t) ww R₁ + C R₂ y(t) (b) Find the poles of the system. (c) Find its unit impulse response h(t). (d) Find its unit step response.

7. } Given the following transfer function for H(s) where it is under damped, for a unit step input Vin(s) = U(t), find the time it takes to reach the first overshoot peak in seconds (use two digits to the right of the decimal place). AQ) q A² + 34 +9

(b) The top panel in Figure 1 shows the input and the impulse response of an LTI system. Sketch the output of the system. Note: No mathematical work is needed, use a graphical approach. x(t) h(t) 2 2 1 1 t -5 -1 1 -3 3 y(t) Figure 1: Figure for Problem 1(b).

For the system shown in figure below, 1-Obtain the overall transfer function 2-Find the rise time,peak time, peak overshoot and settling time if it is subjected to unit step input 3-Obtain an expression for the output response C(t). 4-Comment on the stability of the system by investigation the poles of the system. C(s) 2 R(s) S+2S+3