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Math Help - Simple harmonic motion: origin of the formula v^2=w^2(a^2-x^2)

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    Member ssadi's Avatar
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    Simple harmonic motion: origin of the formula v^2=w^2(a^2-x^2)

    I forgot how this formula v^2=w^2(a^2-x^2) comes in the simple harmonic motion. I mean v^2=w^2 r^2 but then how do you substitute (a^2-x^2) in place of r^2. Something to do with circles. Just couldn't find in the M3 book. Please help me or give me some links where i can find this formula.
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  2. #2
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    Quote Originally Posted by ssadi View Post
    I forgot how this formula v^2=w^2(a^2-x^2) comes in the simple harmonic motion. I mean v^2=w^2 r^2 but then how do you substitute (a^2-x^2) in place of r^2. Something to do with circles. Just couldn't find in the M3 book. Please help me or give me some links where i can find this formula.
    I'd start from the definition: ma = - kx where a is the acceleration. Therefore solve the following differential equation for v (v is velocity): \frac{d}{dx} \left(\frac{v^2}{2} \right) = - \frac{k}{m} x.
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