Question

Please show all work and do not copy other solutions. I will give a thumbs up if you explain everything and get it correct. Thank you.

Express the function y(t)=4 sin 2t + 15 cos 2nt in terms of (a) a sine term only. (b) Determine the amplitude, the period, the frequency in hertz of the function. (c) Draw the function in time domain.

Answer 1

Basics Sin CA+B) = sin(A) COS(B) + COSCA) SINCB) y = AS in (wt+ o) A= amplitude, w = Frequency in radran / second Q = Phase angle waaaf; fa frequency in H₂ f = 74 ; T = Time period 3t 3 ñ zone W= 2 solve to With basic know.ledge, let us question. Given, 2 yct) = -4 sin(24t)+ 15 Cos (zat) - ultiplying by 4² + 15² and divide et by ry², 152 stige ITIN

si Sin(zat) y (t)=√4²715² x u 15 cos (27) Povu+152 15 Cos(zat) I u Sincant) + V241 rzul Suct zul cos 75 ° Ñ Y 0.257 66 - rzul 0.9662 0.9662 sin 75° ~ 15 Jau - 1. uct=240 I Sin cantoCasso) t.cos(zat):Sin(750) / 1 (1) 24Ị Sơn (2 x + 75) - -> T yets a 15.52 sin (2*4 +75) - b) yct) = rzul sin (22+475°) Amplitude A V2y7 15.52 W=2ñ 3) frio => 2a f= 2* ffrequency f = 1 Hz

Time Period: 1= f 1 second y= A sinut) So, y=fzui sin(aat + 75°). or y = r2u1 Sincent +52) 1241 1241 719 V RÝ t-o, yo sau sin(759) – 15 t = 7 7 , ya rau sin(x) = 0

Explanation! Tradrame = 180° = 75°. m x75 radrane 80 > 75° radrans. 5 12 So, to plot any graph, sub different time instants. t=o, y= Vzul Sin (57) Š 15 to Inye szur Sinca) = 0 12 2u ; yo soulson (27) = 0 te t=-5 ; 4= r2u1 sin col=0 24 Since, we got the above values and we have basic relea about sinusoidal ing MATLAB. . we v wave,

%MATLAB CODE

clear all

clc

t=-17/24:0.001:19/24; %Specify time to plot
y=sqrt(241)*sin(2*pi*t + 5*pi/12);
plot(t,y)
grid on
ylabel('Amplitude')
xlabel('time')

Amplitude -0.8 -0.6 -0.4 -0.2 0.2 0.4 0.6 0.8 time