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Math Help - Direct Substitution

  1. #1
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    Direct Substitution

    I've come across some notation that I've never had to deal with, so I'm not to sure what I'm supposed to do.

    I have an equation s(t) = e^{-\frac {t}{2}}cos(2t)

    I'm supposed to show by direct substitution that the displacement satisfies the differential equation

    4\frac{d^2s}{dt^2} + f\frac{ds}{dt} + 17s = 0

    I'm really thrown off by the term 'direct substitution' as we haven't used it in this unit. What am I supposed to substitute into what??
    Also, the notation of \frac {d^2s}{dt^2} is confusing me too - what is this in relation to?

    Also, please, no giving me answers to the equation, I'm moreso after an explanation of what I'm supposed to be doing here...
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  2. #2
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    Re: Direct Substitution

    Hey astuart.

    Basically it's asking you to calculate the derivatives and then substitution those into the equation and show that it equals zero.

    So s = s(t) is your original equation while ds/dt is the first derivative and d^2s/dt^2 is the second derivative.
    Thanks from astuart
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  3. #3
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    Re: Direct Substitution

    Quote Originally Posted by chiro View Post
    Hey astuart.

    Basically it's asking you to calculate the derivatives and then substitution those into the equation and show that it equals zero.

    So s = s(t) is your original equation while ds/dt is the first derivative and d^2s/dt^2 is the second derivative.
    Thank you, that makes sense now
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