794_Dynamics 11ed Manual

794_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics A= −v Chapter 22 B = θ0 ωn L θ = A sin ( ωn t) + B cos ( ωn t) A = −0.101 rad B = 0.30 rad ωn = 4.95 rad s Problem 22-11 A platform, having an unknown mass, is supported by four springs, each having the same stiffness k. When nothing is on the platform, the period of vertical vibration is measured as t1; whereas if a block of mass M2 is supported on the platform, the period of vertical vibration is t2. Determine the mass of a block placed on the (empty) platform which causes the platform to vibrate vertically with a period t3. What is the stiffness k of each of the springs? Given: M2 = 3 kg t1 = 2.35 s t2 = 5.23 s t3 = 5.62 s Solution: Guesses M1 = 1 kg M3 = 1 kg k=1 Given N m t1 = 2π M1 4k ⎛ M1 ⎞ ⎜⎟ ⎜ M3 ⎟ = Find ( M1 , M3 , k) ⎜k⎟ ⎝⎠ t2 = 2π M1 + M2 4k M1 = 0.759 kg t3 = 2π M3 = 3.58 kg k = 1.36 792 N m M1 + M3 4k ...
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