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Math Help - second order differential equations (spring)

  1. #1
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    second order differential equations (spring)

    im doing revision for my calculus and under second order differential equations under springs-free vibrations, i saw this formula R=(beta)(y with a dot on top)
    can anyone tell me what that y with a dot on top means? there is also one with 2 dots on top. i know that the beta is the damping constant. just need help from someone about the y with dots. thanks
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  2. #2
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    Quote Originally Posted by yen yen View Post
    im doing revision for my calculus and under second order differential equations under springs-free vibrations, i saw this formula R=(beta)(y with a dot on top)
    can anyone tell me what that y with a dot on top means? there is also one with 2 dots on top. i know that the beta is the damping constant. just need help from someone about the y with dots. thanks
    Hello yen yen,

    The dot means nothing more than the derivative with respect to time of the variable you're looking at, p.e.

    \dot{x}=\frac{dx}{dt}

    double dots mean: take the derivative twice...

    hope this helps,

    Coomast
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  3. #3
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    Quote Originally Posted by Coomast View Post
    Hello yen yen,

    The dot means nothing more than the derivative with respect to time of the variable you're looking at, p.e.

    \dot{x}=\frac{dx}{dt}

    double dots mean: take the derivative twice...

    hope this helps,

    Coomast
    oh. so y with a dot on top is the same as y'? silly me... should have paid attention in lectures. thanks
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  4. #4
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    No, the dot means to take the derivative with respect to time, an accent means with respect to another variable, p.e. x (it can also mean time t though). They both mean indeed the derivative but the dot is used more in mechanics (time), while the accent is used more in mathematics (any variable, p.e. x or t). Is this clearing the difference?

    It can be confusing, and to be honest I do not know why they use a different symbol for the time derivative in mechanics. In math this difference is not made, at least as far as I know.

    Coomast
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