very basic maths help

Discussion in 'Math' started by harry99932, Jan 2, 2011.

  1. harry99932

    Thread Starter Member

    Dec 30, 2010
    38
    2
    Hi guys can someone help me out im a verrrrrrry un mathematically minded person slowly learning lol Im trying to expand out this equation but not sure how to go about it.

    Vout= Vin* [98+((2/k)*Vin)]

    I think im right so far in thinking il end up with;

    Vin*98 + Vin*(2/k) + Vin*Vin

    Now if thats right, then for the 3rd part of the equation were

    Vin= 0.01 sin(2pi800)

    i get an equation of the type

    (sinx)*(siny)= cos(x-y) - cos(x+y)

    How do i apply this to 0.001 sin (2pi800) ? i.e what do i do with the two 0.001's etc?

    Please help im very lost:D
     
  2. edgetrigger

    Member

    Dec 19, 2010
    133
    19

    just this => Vin*98 + Vin*(2/k) * Vin
     
  3. edgetrigger

    Member

    Dec 19, 2010
    133
    19
    correct formula is

    sinx * siny = 1/2 * [cos(x-y) - cos(x+y)]
     
  4. edgetrigger

    Member

    Dec 19, 2010
    133
    19
    i could not get what you want to do with Vin.

    If Vin is a sine wave the equation would be Vin = Vmax* Sin(θ+phy)

    [ i did not get the symbol for phy in ]

    could you pls let me know what you want to do with Vin
     
  5. harry99932

    Thread Starter Member

    Dec 30, 2010
    38
    2
    Hi edgetrigger,

    The 0.01 sin(2*pi*800) is definatley correct. Peak sine wave voltage is 0.01 at 800hz working from equation; Vpeak sine (ωτ) were t is irrelevant for now and 2*pi*800 is hertz to angular velocity

    the equation is the input to output expression for a theoretical amplifier, were v out = the equation given below, the answer should be several (3 we think) voltages a dc component, fundamental frequency and a harmonic frequency.

    The previous example we are given is

    Vo= 0.001 + 9.962Vi + 0.1Vi^2 with Vin at 0.01 sin (2000*pi*t) we get a result of

    0.001005 + 0.09962sin(2000*pi*t) - 5x10^-6cos(4000*pi*t)

    0.001005 volts dc
    0.09962 volts ac at 1000hz fundamental frequency
    5x10^-6 volts ac at 2000hz second harmonic

    Any ideas??
     
  6. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    The answer is delayed, but, hey, I deserve some christmass free time.

    Let me try this one:

    <br />
V_{out}=V_{in}(98+\frac2kV_{in})\\<br />
=98V_{in}+\frac2kV_{in}V_{in}\\<br />
=9.8\sin (1600\pi t) +\frac2k 0.0001 \sin^2 (1600 \pi t)\\<br />
9.8 \sin(1600 \pi t) + \frac2k 0.0001 \left( \frac12 (1- \cos (3200 \pi t)) \right )\\<br />
=\frac{0.0001}{k}+9.8 \sin (1600 \pi t)- \frac{0.0002}{k} \cos (3200 \pi t)<br />

    So, I guess your assumptions where correct.

    I used the formula proposed by edgetrigger.

    As usual, any corrections are welcome.
     
  7. harry99932

    Thread Starter Member

    Dec 30, 2010
    38
    2
    thanks for that georacer and edge trigger, i got there in the end with a lot of head banging but your workings make a lot more sense than mine so nice to see how i got there:D
    Really appreciate the help, its nice people like you that will eventually help us mere mortals kill maths once and for good:D

    Happy new year
     
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