I've searched through about 5 math books but don't know how to start this one:(adsbygoogle = window.adsbygoogle || []).push({});

I have a drumskin of radius a, and small transverse oscillations of amplitude:

[tex] \nabla^2 z = \frac{1}{c^2}\frac{\partial^2 z }{dt^2} [/tex]

Ok, so I can write the normal mode as

[tex]z=Z(\rho)cos(\omega t) [/tex]

Questions:

1) If I want to find the differential equation for [tex]z=Z(\rho) [/tex], do I just plug the second equation into the first, but use the polar coordinate version of nabla?

2) If I want to obtain an estimate for the lowest normal mode frequency using a trial function of form [tex]a^{\nu}-\rho^{\nu}[/tex] with [tex]\nu[/tex] an adjustable parameter...where do I start???

Thanks!

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# Drumhead PDE

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