Mass-Spring - Graph - Transfert function

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"1) Mass-spring m=massk=stiffness1 ? The natural frequency fn is? ? = 2? ? Now apply a downward 1 G body load on the mass. The static deflection equation is:? ? = ? ?? ? ? =? 1 ? ? ? =2? ? Period:? ? ? = 2?? 2) Graph Initial conditions: t=0 x=0 and v..

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"1) Mass-spring m=massk=stiffness1 ? The natural frequency fn is? ? = 2? ? Now apply a downward 1 G body load on the mass. The static deflection equation is:? ? = ? ?? ? ? =? 1 ? ? ? =2? ? Period:? ? ? = 2?? 2) Graph Initial conditions: t=0 x=0 and v=0D=0.2m andG=1kg? ? ? = ? sin ? ?3) Transfert function ? ? + ? = ? ?? Laplace transform:? 2? ? ? + ? ? = ? ? (? )?? ? ?? ? = =? 2 ? ? ? + ? 4) Phase and magnitude ? ?? ? ? = =? ? 2 2 (? ? ) + -? + ? ? ?? ? ?=? 2 -? + ? ? = arg ? ? ?= 2? ? 5) a) camera:1 ? =2 ? 1 - ? ? ? = 100? ? = 60? = -0.5625? ? = 80? = -1.7778? ? = 120? = 3.2727So better is the 60hz, after the 80 and last 120hzb) Engine:1 ? =2 ? 1 - ? ?? = 12? ? = 6? =-0.3333? ? = 8? = -0.8000? ? = 10? = -2.2727So better is the 6hz, after the 8 and last 10hzc) Comparison1 ? ? ? =2? ? K=m1 ? 1 ? 1 = = ? ?2? ? 2? 1 ? /2 ? 2 = = ? 1/ 22? ? The first system has higher natural frequency Ratio=1/ 2 "

Bernoulli Principle at the lake point and the Reservoir Point

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