Problem 4 (P-2.9 a, b) [10] x(t) = 2 sin(w。t + 45°) + cos(wt) a) Express x(t) in the form x(t) = A cos(w¸t + ¢) [5]. b) Assume @=5π rad/s. Plot x(t) between -1≤ t≤2 using Matlab/Octave [5].

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For the system described in problem 1, what is the steady-state error for the ramp input r(t) 10tu (t)? %3D Edit View Insert Format Tools Table

tem is shown in the figure. Outp s(s+3)

Write a differential equation in v(t).

answer A and B.

Q2 TM UTM 4 (t) UTM UTM U. 10Ω 5 UTM V, (t) = 100cos (20t + 30°)V 0.5 H 5 UTM UTM ở G UTM UTM 0.05 F TM UTM UTM UTM 3 UTM & UTM UTM Figure Q2 For the AC circuit in Figure Q2, TM@UTM Draw the frequency/phasor domain equivalent circuit. UTM & UTM O UTM &UPain UTM (b) Compute the total impedance of the circuit. TM O UTM (c) Find Is and expressed the current in time domain. 8 UTM UTM 증 5 UTM (d) What will happen to the total impedance when the alternating current (A UT source V1 is replaced with a direct current (DC) voltage source. UTM &UTM & 10

is(t) = A₁ cos s (1000 + 77) + A₂ ⋅ cos ( s (2000t - 7/7) Assume the system is in steady state. Find the current ia at times t₁ = 4πms: iα(t₁) = B₁ t25π ms: ia(t₂) = B₂ is(t) Given Variables: A1:2A A2:1A L: 2 mH C: 500 uF R1:2 ohm R2: 2 ohm K: 5 V/A Determine the following: B1 (A): B2 (A): www kia(t) R₁ |ia(t) C -R₂ ✗

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