Algerbraic Methods: Instantaneous voltages

Discussion in 'Math' started by Biggsy100, Jul 10, 2014.

  1. Biggsy100

    Thread Starter Member

    Apr 7, 2014
    88
    1
    I don't even know where to start with this question:

    The instantaneous value, y(t) of a damped oscillation is described by the following formula:

    y(t) = e^-t/tsin(2pit/t)

    I know t = time in seconds, tau= time constant in seconds, T =Periodic time in seconds.

    I need to count the following to 3 decimal places with the value y(t) for the following conditions:

    t= 0.002 seconds
    Tau = 1.6 Seconds
    T = 50 Milliseconds

    I don't expect someone to do this for me, but could someone suggst a method to start a process?
     
  2. Papabravo

    Expert

    Feb 24, 2006
    10,148
    1,791
    Your formula makes no sense because there is no tau and there is no T. There are three occurrences of lowercase t and a curious division symbol that makes your function quite pathological for t = 0 and t an integer multiple of 2*pi. Ask your question again and maybe render the equation in TeX.
     
  3. studiot

    AAC Fanatic!

    Nov 9, 2007
    5,005
    513
    Just to echo Papabravo's comments:

    Your equation is missing a constant to make your equation dimensionally consistent.

    What are the units of y(t)?

    If you can't create the LAtex to display the formula correctly, describe it properly in words and someone here will help. Alterntively use stars for all multiplications and sufficient brackets to show things properly.
     
  4. Biggsy100

    Thread Starter Member

    Apr 7, 2014
    88
    1
    Hi guys,I simply have the description as what originally said and the formula is written:

    y(t) = e^-t/tau sin (2pit/T)
     
  5. studiot

    AAC Fanatic!

    Nov 9, 2007
    5,005
    513
    I said, and I meant, that your formula is dimensionally inconsistent.

    The exponential is a pure number, as is the sine so their product is also a pure number.

    So the right hand side is a pure number.

    Theleft hand side is a voltage.

    I also said you are missing a constant from this equation. The constant has the units of voltage and makes everything correct. This constant is the amplitude at t=0 or the amplitude for all t in a non dissipative system.

    Writing maths on one line leads to errors and I strongly recommend against it.
     
  6. Biggsy100

    Thread Starter Member

    Apr 7, 2014
    88
    1
    Ok, thank you. But it's not 'My' formula...I am just literally reading from a paper.
     
  7. Papabravo

    Expert

    Feb 24, 2006
    10,148
    1,791
    What you have written is still ambiguous. How's about:

    y(t) = e^(-t/tau)*sin((2*pi*t)/T)

    At least nobody could think that i was the imaginary unit.
     
    Biggsy100 likes this.
  8. DerStrom8

    Well-Known Member

    Feb 20, 2011
    2,428
    1,328
    I suggest you learn how to use the LATEX editor. When you go to make a post, click the "Go Advanced" button at the bottom, and then click the Sigma button as shown below.

    2014-07-11 16_03_35-All About Circuits Forum - Reply to Topic.png

    As previously mentioned, writing all of the math on one line will lead to errors and confusion, especially if you don't include enough parentheses, as you have not.
     
    Biggsy100 likes this.
  9. MrAl

    Well-Known Member

    Jun 17, 2014
    2,438
    492
    Hi,

    I would go with:
    y(t)=e^(-t/tau)*sin((2*pi*t)/T)

    where
    t is time,
    tau is a time constant,
    T is the period of the sinusoidal part also equal to 1/f.

    Also, the units of volts is implied as is often the case if the context really did imply that and so we dont really need anything else except maybe a note that states the units if there really is a chance of confusion :)
     
  10. studiot

    AAC Fanatic!

    Nov 9, 2007
    5,005
    513
    That doesn't alter the fact that the equation, as stated, is missing a constant.

    Also please note the the OP has transferred discussion to his other thread.

    http://forum.allaboutcircuits.com/showthread.php?t=99340
     
  11. MrAl

    Well-Known Member

    Jun 17, 2014
    2,438
    492

    Hi there,

    What constant are you referring to?
     
  12. studiot

    AAC Fanatic!

    Nov 9, 2007
    5,005
    513
    The formula comes from the general solution to damped oscillation

    Vinstantaneous = exp(-ωt) (Asin(ωt) + B cos(ωt+ψ))

    where A and B are constants of integration and have the dimensions of voltage.

    The authors of the question have chosen boundary conditions so that B=0 volts and A=1volt.

    A is, of course, the amplitude of the initial oscillation at t=0; the usual formula for a voltage sinusoid is, of course V= Va sin(ωt)
     
Loading...