Adding 2 voltages using trig

Discussion in 'Homework Help' started by skitzo2crazy, Jan 8, 2010.

  1. skitzo2crazy

    Thread Starter New Member

    Nov 28, 2008
    3
    0
    My homework Question is:


    a) Two voltages 75.sin(ωt-2pi/3) and 50.sin ωt are added together, determine the resuting voltage.

    b) Then determine the first time the resulting voltage has an amplitude of 30V, given that the frequency of each of the individual waves is 25 Hz.

    I get the answer "66.14sin (ωt-79.1) for part a.
    However I am stuck on part b. Can anybody help me solve part b?
    (I bet its easy but my mind has gone blank!)
     
  2. hgmjr

    Moderator

    Jan 28, 2005
    9,030
    214
    Assuming that the answer you have for the sum is correct, you should be able to substitute the value 2*pi*25 in place of ω and then set the equation equal to 30 and solve for t.

    hgmjr
     
  3. skitzo2crazy

    Thread Starter New Member

    Nov 28, 2008
    3
    0
    I get 157.07 for 2*pi*25

    I then use t=2*pi/ω to get 0.039s

    But I am confused as to where the 30v comes into it?
     
  4. hgmjr

    Moderator

    Jan 28, 2005
    9,030
    214
    The periodic nature of a sinusoidal function means that it takes on the same value at various points in time. This problem is asking you to find the value of the variable time t at which the equation takes on the value 30V for the first time. That is why you need to set the equation equal to the value 30V.

    hgmjr
     
    Last edited: Jan 10, 2010
  5. skitzo2crazy

    Thread Starter New Member

    Nov 28, 2008
    3
    0
    I got there in the end.
    Thank you for your time and your patience.
     
  6. zgozvrm

    Member

    Oct 24, 2009
    115
    2
    Assuming the θ values are in radians, I got 66.14 sin (ωt-1.38).
    It looks like you forgot to convert degrees back to radians
    (-1.38 rad = -79.1 deg)

    Otherwise, if the θ values are in degrees, I get 124.95 sin(ωt-1.26)
     
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