tsl299 - = r k m-b 2 4 m 2 (b) overdamped motion : b 2...

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Mechanical Oscillator with Damping law of motion: F = ma, a = d 2 x dt 2 law of force: F = - kx - bv, v = dx dt equation of motion: d 2 x dt 2 + b m dx dt + k m x = 0 Solution for initial conditions x (0) = A, v (0) = 0 : (a) underdamped motion : b 2 < 4 km x ( t ) = Ae - bt/ 2 m » cos( ω 0 t ) + b 2 0 sin( ω 0 t ) with
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Unformatted text preview: = r k m-b 2 4 m 2 (b) overdamped motion : b 2 &gt; 4 km x ( t ) = Ae-bt/ 2 m cosh( t ) + b 2 m sinh( t ) with = r b 2 4 m 2-k m tsl299 p.1/1...
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This note was uploaded on 04/30/2008 for the course PHYS 204 taught by Professor Andrevantonder during the Spring '07 term at Rhode Island.

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