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# SolSec1.5 - Problems and Solutions Section 1.5(1.57 through...

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Problems and Solutions Section 1.5 (1.57 through 1.65) 1.57 A helicopter landing gear consists of a metal framework rather than the coil spring based suspension system used in a fixed-wing aircraft. The vibration of the frame in the vertical direction can be modeled by a spring made of a slender bar as illustrated in Figure 1.20, where the helicopter is modeled as ground. Here l = 0.4 m, E = 20 × 10 10 N/m 2 , and m = 100 kg. Calculate the cross-sectional area that should be used if the natural frequency is to be f n = 500 Hz. Solution: From Figure 1.20 ω n k m EA lm = = and ω π n = = 500 3142 Hz 2 rad 1 cycle rad/s Solving for A yields: A lm E A n = = ( ) ( )( ) × = = ω 2 2 10 3142 4 100 20 10 0 0019 19 . . m cm 2 2

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1.58 The frequency of oscillation of a person on a diving board can be modeled as the transverse vibration of a beam as indicated in Figure 1.23. Let m be the mass of the diver ( m = 100 kg) and l = 1 m. If the diver wishes to oscillate at 3 Hz, what value of EI should the diving board material have? Solution: From Figure 1.23, ω n EI ml 2 3 3 = and ω π π n Hz = = 3 2 6 rad 1 cycle rad/s Solving for EI EI ml n = = ( ) ( )( ) = ω π 2 3 2 3 6 100 1 3 11843 5 . Nm 2 1.59 Consider the spring system of Figure 1.28. Let k 1 = k 5 = k 2 =100 N/m, k 3 = 50 N/m, and k 4 = 1 N/m. What is the equivalent stiffness?
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