Question

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4.) Find the amplitudes of each of the following harmonic synchronous oscillations and the phase angle between the oscillations. (20 pts) xi(t) = 3cos(20t) - 4sin(20) x:(t)= 1.5sin(20t - 1/6) - 2cos(20t) 5.) Represent the two harmonics from problem #4 in the time domain, frequency domain, using phasors and complex numbers. (20 pts) 6.) Calculate the amplitude and the phase of the oscillation that results from the composition of the two harmonic synchronous oscillations in problem #4. (10 pts)

Answer 1

— е 3 + + zjetet -zje tot +(22-24) & hot wild 5 530 2 Cos2ot 7 4 Lessot frot] +91) = 3 cos(20+) – 4 sin 20t 22 [eizst+ e fot] - fot Zetot + I, t) = (2+24) ethet 4 = 3 + 24 Kol = 594 + 4 4,23-24 Kel= d. - tean (2/3/2) = ten - teen teen' 14/3) = -53 b) alt) = 1:5 sin (206-7/6)-2 cos zot = 105 (sin zot Los 30 - cosasin3o) 302 sinnot (2 2 + 2) coszot 3. [eiset evrot + ] -4 4 4 [etrotte e-isot 353 (W) (232014 -obat) - -11 leiset -3JB ; 23204 + 353 y efrot hetzot i 303 Prot +( C 1-1-1-2-31) -11+3134 14,1 =152] = 1152 0,3 toll 300 x ) -1800 = 2512899–180° = -159,716° 02= R0 = 180-25: 284 = 154.716 Žj 2 frot - serot 355 - e + Regi) e poi C-l 8

n! cn - an23, 5)(a) selt) = cot en Losnwot -6) anyon bna-an 디스를 452 2.54 53° Cal = 3 - 12 = 2.52-530 ca 22 - jan x,(t) --4m ) cos (nwot-58°) 3 nal b) 의 X2(t) = 1.5 sin 1.5 Sin (206" @ l - 265(206) All - Buy 1.52 241540716 8 C-1 8 + ಖ್ಯಾತ 1:52 Z+54.716 phase domain 4334 time domain

by as alt) = 3 cos (20t) - 4 sin(20t) dalt) = 3 coshot) + 4 cosporrot) dit) 320 + 4L30° Amplitude (A) - J3P+ 14 cost 5 1 arest 360s not Phase (4) = goo b) Xt) = 115 Sin (20 t-7) - 2 Cos/20t) Iz(t) = 1.5 sin (2017) + 2 sin (rot-go) A = Ja2fb² trabcoso 4.5)2 +10° +2x115x24.6053000 5 2.25 + 4 + 6 x ۱۱: & sinrot 300 > sinpet - 11:446 3.38 Sin zot-g = 30°