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How Do PE and KE Interact in a Vibrating String?

Thread starter unscientific
Start date Apr 14, 2013
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String Vibrating

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3 replies · 2K views · last reply Apr 18, 2013

unscientific

Thread starter
Apr 14, 2013

#1

Homework Statement

Printed exam question 9 on a vibrating string: wave equation for transverse displacement with separation of variables, string fixed at x = 0 and x = a, initial displacement sin(2πx/a)(1 + cos(2πx/a)), and a request for kinetic and potential energy.

Homework Equations

The Attempt at a Solution

Handwritten equations: phi = sin(3pi x / a) cos(2 v pi t / a) + (1/2) sin(4pi x / a) cos(4 v pi t / a); V = (1/2) T integral from 0 to a of (d phi/dx)^2 dx; T = (1/2) rho integral from 0 to a of (d phi/dt)^2 dx.

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Discussion

unscientific

Apr 15, 2013

#2

bumpp

unscientific

Apr 17, 2013

#3

any ideas to show how they are independent of time? (Other than brute-force integration)

unscientific

Apr 18, 2013

#4

bumpp

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