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# L11 - Vibrations Hookes Law Force = k Elongation...

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Vibrations Weight of mass g Equilibrium position u = 0 mg mu ” = mg - k ( L + u ) = - ku - kL mg Hooke’s Law: Force = k × Elongation - kL + mg = 0 u ( t ) - k ( L + u ( t ) L

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Weight of mass g Equilibrium position u = 0 mu ” = - ku - γu - γu Beer mg - kL - kL + mg = 0 mg - k ( L + u ( t )) Hooke’s Law: Force = k × Elongation L u ( t ) 2
Weight of mass g Equilibrium position u = 0 - γu Beer mg - k ( L + u ( t )) F ( t ) mu ” = - ku - γu + F ( t ) mu ” + γu + ku = F ( t ) - kL Hooke’s Law: Force = k × Elongation mg - kL + mg = 0 u ( t ) L 3

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is mu 00 + γu 0 + ku = F ( t ) . ( DN ) Example: The Undamped Case If γ = 0 the equation becomes mu 00 + ku = F ( t ) , ( UN ) whose associated homogeneous equation mu 00 + ku = 0 ( UH ) has FS { cos( ω 0 t ) , sin( ω 0 t ) } , where ω 0 def = p k/m is the natural frequency or eigenfrequency of the spring–mass system. If
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L11 - Vibrations Hookes Law Force = k Elongation...

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