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Math Help - Curves and Damped harmonic motion 0_o'

  1. #1
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    Curves and Damped harmonic motion 0_o'

    I have to find an equation/model for the following:

    A vibrating spring has damped harmonic motion- the oscillations decrease over time

    -The centre of vibration is 0
    -The starting amplitude of vibration is 0.6mm
    -after 5 seconds the amplitude decreases to 0.5 mm
    -During this time the spring moved forward and backwards 200 times

    My attempt-
    it will be a sine curve as centre of vibration is 0
    The general form will be y=Ae^ax sin bx
    200 forwards and backards= 100 cycles
    if 100 cycles in 5 seconds then it is 100/5= 20 cycles per second = frequency (f)
    T=1/f and T= 2pi/b and found b to be: 40pi
    A=0.6? i.e. initial amount

    It was 0.6 at 0s
    0.5 at 5s

    (0.5/0.6)=Ae^5x/Ae^0x
    (A's cancel) therefore:
    (0.5/0.6)=e^5x/e^0x
    e^5x-0x=0.5/0.6
    x= -0.036464

    Can anyone tell me if I'm on the right track please , Im not sure if all of my working out is valid? if not could you please give the correct working out.
    Thanks
    Mathhelp246
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  2. #2
    MHF Contributor
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    Re: Curves and Damped harmonic motion 0_o'

    Hey Mathshelp246.

    For this problem, do you need to use some kind of parametric function?

    The reason I ask is that typically for a lot of these kinds of problems, you have specific parametric Differential Equations (DE's) that specify say a damped spring with certain parameters.

    If you have that model and have been taught it in class, then I suggest you post it here so we can look at it.

    Typically you will take this model (which has a number of free variables) and you will set those to either constants or functions and solve for your final value.
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  3. #3
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    Re: Curves and Damped harmonic motion 0_o'

    Thanks for the reply chiro =)

    Um the question asks to form a model based on your knowledge of curves, amplitude, frequency and period
    and all the information that it gives is that what is listed above:

    "A vibrating spring has damped harmonic motion- the oscillations decrease over time

    -The centre of vibration is 0
    -The starting amplitude of vibration is 0.6mm
    -after 5 seconds the amplitude decreases to 0.5 mm
    -During this time the spring moved forward and backwards 200 times"

    I think that it is based on curves like
    Ae^-kx sin bx
    Ae^-kx cos bx

    I think they want it in an exponential model
    " The exponential function is an important model of many natural systems, as are the periodic functions sine and cosine"
    The combined functions e^ax sin bx and e^ax cos bx are also important in many applications, with many oscillations and vibrations being closely modelled by these funtions. VIbrations can be modelled by y=Ae^-kx sin bx and y=Ae^-kx cos bx, where k is negative - damped harmonic motion"
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  4. #4
    Forum Admin topsquark's Avatar
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    Re: Curves and Damped harmonic motion 0_o'

    It might help to note that y = e^{-at}sin(bt) not a function of x.

    -Dan
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