Single-frequency analysis 2. Derive the 'accurate' amplitude and phase responses of the first-order pole system at...
F Fosin t m k 2 Figure Qla: System is subjected to a periodic force excitation (a) Derive the equation of motion of the system (state the concepts you use) (b) Write the characteristic equation of the system [4 marks 12 marks (c) What is the category of differential equations does the characteristic equation [2 marks fall into? (d) Prove that the steady state amplitude of vibration of the system is Xk Fo 25 + 0 marks (e) Prove that...
Explain Frequency Domain Analysis, Amplitude and phase frequency characteristics, its mathematical and physical interpretation in control engineering.
signals and systems
The figure shows the pole diagrams and frequency responses of four continuous-time LTI systems. But they are out of order. Match each pole diagram with its frequency response POLE-ZERO DIAGRAM FREQUENCY RESPONSE POLE-ZERO DIAGRAM1 FREQUENCY RESPONSE1 0.4 0.35 0.3 0.25 0.15 0.1 0.05 3 2.5 -2 1.5.5 00.5 -6 42 POLE-ZERO DIAGRAM 2 FREQUENCY RESPONSE 2 0.6 0.5 0.4 0.3 10 -10 0.1 -3 -2.5 -2 1.5-0.5 0 0.5 -6 -42 POLE-ZERO DIAGRAM 3 FREQUENCY RESPONSE 3...
- Frequency Response (Amplitude Response only). Hz). with frequency, 22. for a discrete time system shown below. *(-1) - x[-2] - ... -0 and yf-1) - Y[-2] ... - x[r] - int) Find “Math Model" for the system. nt) Find "Transfer Function" for the system. Draw the pole-zero plot for the system (use unit circle on Re-Im axis) Sketch the amplitude response of the system → indicate values at important points (92 = 0, 1/4, 21/4, 37/4, T) include detailed...
2. Consider a second IIR filter a. Determine the system function H(z), pole-zero location (patterns), and plot the pole-zero pattern. b. Determine the analytical expression for frequency response, magnitude, and phase response. c. Choose b so that the maximum magnitude response is equal to 1. d. Plot the pole-zero pattern and the magnitude of the frequency response as a function of normal frequency.
2. Consider a second IIR filter a. Determine the system function H(z), pole-zero location (patterns), and plot...
Below is the frequency response of a dynamic system +)20 20 → 1st order 40">2"d Order a. What are the corner frequencies? 、.a.,.1D.歩100 b. How many poles in the system? e. How many zeros in the system'? d. For the input signal shown in the Figure below find (at steady-state situation): i. The output signal amplitude ii. The output signal phase (in degrees and show the sign)... Plot the output signal on the Figure below e. 57 58 9 61...
Discuss the effect of the frequency of the driving force on the amplitude and phase of the oscillator, by deriving the solution of the relevant differential equation. A spring stretches by 1.96 m when a 2 kg mass is attached. The system is then submerged in liquid which imparts a damping force numerically equal to 4 times the velocity of the mass. Find the value of the steady state solution after T/2 second if an external force f(t)= 2sin 2t(kg.m/sec2)...
Question One (a) The Impulse Response of a second order system is given by h(t) where: h (t) 4000 e 3000 e20 where the time, t, is given in milliseconds (ms) and h(t) is considered to be the resulting voltage in volts. (0) Derive the Transfer Function, the Laplace Transform H(s) of h(t). (i) Using part (0, write out the Frequency Response, H(jo), of the second order (ii) Express the Frequency Response obtained in part (i) as a single response...
Signal And System
Build a first order LPF with cut-off frequency at 10 kHz. A simple low pass filter (first order) circuit is shown in Figure 1. V = gain 0.7 (a) RC low Pass Filter Circuit Figure 1 (b) Frequency ResponseCurve show that the impulse response for a first order low-pass filter in Figure 1 is given by 1 H(f) = 1+j295RC The cut-off frequency for a low-pass filter is fcutoff ZRC Generate a rectangular pulse with frequency of...
2. A first-order temperature measurement system is excited by a 0.25Hz sinusoidal input (a). Knowing the time constant is 4 second, and the indicated amplitude is 10 °F, find the true temperature, (b) if the dynamic frequency is 20Hz, what will be the required time constant?
2. A first-order temperature measurement system is excited by a 0.25Hz sinusoidal input (a). Knowing the time constant is 4 second, and the indicated amplitude is 10 °F, find the true temperature, (b) if...