A sinusoidal function is described: (the custom diagramfunction is currently dow

Question

A sinusoidal function is described: (the custom diagramfunction is currently down) y axis : i (t) x axis: t -the sinusoidal curve is 4 mA at t = 0. -it then rises up to peak at 10, then starts to travel downthrough x axis and bottoms out at -10, then travels back up to 10, thenfinally curves down again to x axis. KEY INFO: the distance between top 2 peaks is 21.6 ms(horizontal distance)                      theheight from bottom curve to top curve is 20 mA (verticaldistance) The question then is: Determine the frequency, phase,and amplitude for expressing this sinusoid in the standard form -->    i(t)=Ipcos(t+) A sinusoidal function is described: (the custom diagramfunction is currently down) y axis : i (t) x axis: t -the sinusoidal curve is 4 mA at t = 0. -it then rises up to peak at 10, then starts to travel downthrough x axis and bottoms out at -10, then travels back up to 10, thenfinally curves down again to x axis. KEY INFO: the distance between top 2 peaks is 21.6 ms(horizontal distance)                      theheight from bottom curve to top curve is 20 mA (verticaldistance) The question then is: Determine the frequency, phase,and amplitude for expressing this sinusoid in the standard form -->    i(t)=Ipcos(t+)

Explanation / Answer

(a) Standard Form of Sinusoid Current   i(t) = Ip cos(wt+)          has the following property.                        Ip = maximum (positive) value ofi(t)       (Obtained when wt+ =2n+0)                        -Ip = minimum (negative) value ofi(t)      (Obtained when wt+ =2n+)                       At t = 0 ,   i(t) = Ip cos() => = cos-1 (i(t)/Ip)                       Frequency w = 2/T where T = time period betweenconsecutive maxima or consecutive minima Comparing these facts with given problem we have ,   Ip = 10mA       ( Since Maximumpositive (or negative value ) of i(t) = 10 mA or -10mA)                 w = 2/(21.6ms)    ( Since Time periodbetween two maxima = 21.6 ms)                  => w = 2*3.14159*1000/21.6 rad/s = 290.88rad/s Finally at   t = 0s , i(t) = 4mA => = cos-1(4/10) = 66.42 degrees =1.159 radians Hence     i(t)   = { 10 cos ( 290.88(rad/s)*t + 1.159rad ) }mA I hope this helps you

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