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Math Help - Vibration of a wine glass

  1. #1
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    Vibration of a wine glass

    A model for the vibrations of a wine glass is
    x + λx˙ + (ω^2)x = 0
    Suppose that when struck the wine glass vibrates at 660 Hz (about the second E above middle C on a piano). Show that. √(4ω^2 − λ^2) = 2640π
    If it takes about 3 seconds for the sound to die away, and this happens when
    the original vibrations have reduced to 1/100 of their original level, show that
    λ =(2 (log 100))/3
    and hence that λ = 3.07 and ω = 4.15 x10^3(both to three significant figures).
    The glass can stand deforming only to x nearly equal to 1. A pure tone at 660 Hz is produced and aim at the glass,forcing it at its natural frequency so that the vibration are now modelled by x + λx˙ + (ω^2)x = cos(1320pi t)(10^((D/10)-8))/3
    How large should the sound be in order to shatter the glass?
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  2. #2
    Grand Panjandrum
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    Re: Vibration of a wine glass

    Quote Originally Posted by kanezila View Post
    A model for the vibrations of a wine glass is
    x + λx˙ + (ω^2)x = 0
    Suppose that when struck the wine glass vibrates at 660 Hz (about the second E above middle C on a piano). Show that. √(4ω^2 − λ^2) = 2640π
    If it takes about 3 seconds for the sound to die away, and this happens when
    the original vibrations have reduced to 1/100 of their original level, show that
    λ =(2 (log 100))/3
    and hence that λ = 3.07 and ω = 4.15 x10^3(both to three significant figures).
    The glass can stand deforming only to x nearly equal to 1. A pure tone at 660 Hz is produced and aim at the glass,forcing it at its natural frequency so that the vibration are now modelled by x + λx˙ + (ω^2)x = cos(1320pi t)(10^((D/10)-8))/3
    How large should the sound be in order to shatter the glass?
    Well, what have you tried? What is the general solution to the homogeneous equation?

    CB
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