9.1 Consider the sinusoidal voltage v(t) = 40 cos(100pi t +...

9.1 Consider the sinusoidal voltage v(t) = 40 cos(100pi t + 60^circ) V. a) What is the maximum amplitude of the voltage? b) What is the frequency in hertz? c) What is the frequency in radians per second? d) What is the phase angle in radians? e) What is the phase angle in degrees? f) What is the period in milliseconds? g) What is the first time after t = 0 that v = -40 V? h) The sinusoidal function is shifted 10/3 ms to the right along the time axis. What is the expression for v(t)? i) What is the minimum number of milliseconds that the function must be shifted to the left if the expression for v(t) is 40 sin 100pi t V?

Transcript

00:01 In this example, we're going to be working with a sinusoidal function.

00:05 And what this shows is my voltage as a function of time.

00:11 Vt equals 40, cosine, 100 pi t, plus 60 degrees, v.

00:26 So this function represents an oscillating voltage.

00:30 And we're going to be answering a bunch of questions about this voltage in an oscillating system.

00:37 The first thing i want to find is my maximum amplitude of voltage, a max.

00:44 If we compare our equation to the standard equation for an oscillating system, let's use a dummy variable.

00:52 Some function of t equals amplitude times cosine of omega, that's angular, velocity.

01:02 P plus fee, where these are our phase angle.

01:06 Okay, and we know that the cosine function varies between negative one and one.

01:12 So at its maximum value of one, our amplitude will be 40 volts.

01:20 If we go yes, so that's the 40 from our equation.

01:24 And our minimum voltage is going to 40 bolts.

01:28 Question 2.

01:30 Let's to know what is my frequency in hertz.

01:34 Again, we can refer back to this standard form here.

01:38 Compare it to our equation.

01:40 And we see omega equals 100 pi.

01:47 That's my angular frequency.

01:49 I also know that 2 pi f equals omega or f equals omega.

01:58 Over 2 pi.

02:00 So frequency just equals 50 hertz.

02:06 Okay.

02:06 The third question is actually asking for omega and we know that that equals 100 pi radians per second or that 314 rad for a second.

02:21 The next thing i want to find is the phase angle or phase shift of this oscillation.

02:27 Again, comparing with our standard form we see that fee is our phase shift and that's going to be 60 degrees we just see there so d phase shift fee equals 60 degrees and we want that in radiance as well i know 2 pi radiance equals 360 degrees that'll equal xx radiance over 60 we see 60 degrees equals pi over three radiance.

03:01 So that's my phase shift in angle and degrees.

03:04 Next thing i want to find is my period in milliseconds.

03:08 That was part e.

03:10 And we know period equals one over frequency.

03:13 Our frequency equals 50 hertz.

03:19 So my period equals 20 milliseconds.

03:23 All right...

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