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Math Help - Could Someone Please Help Me With This Applied Differentiation/Integration Question

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    Unhappy Could Someone Please Help Me With This Applied Differentiation/Integration Question

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    Last edited by charlottewill; March 15th 2012 at 02:52 AM.
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    Re: Could Someone Please Help Me With This Applied Differentiation/Integration Questi

    Start by letting L = 4r. You then have a function in two unknowns. The maximum will be at points where the partial derivatives are 0 and the Hessian is negative definite, or if you can show the function is concave at that point.
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    Re: Could Someone Please Help Me With This Applied Differentiation/Integration Questi

    Quote Originally Posted by charlottewill View Post
    Please could somebody help me with this tutorial equation

    The velocity (v) of a piston is related to the angular velocity (ω) of the crank by the relationship v = ωr{sinθ+(r/(2L))(sin2θ)} where r is length of crank and L is length of connecting rod. Find the first positive value of θ for which v is a maximum, for the case when L = 4r.

    Regards,

    Charlotte
    \frac{dv}{d\theta}=\omega r \cdot \left(\cos \theta \sin\2 \theta +2 \cos 2\theta \left(\sin \theta +\frac{r}{2L}\right)\right)

    \frac{dv}{d\theta}=0 \Rightarrow \cos \theta \sin\2 \theta +2 \cos 2\theta \left(\sin \theta +\frac{r}{2L}\right)=0

    for L=4r you have :

    \cos \theta \sin\2 \theta +2 \cos 2\theta \left(\sin \theta +\frac{1}{8}\right)=0
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