Solve this ? For the system shown in Fig. 4.2.7, derive the equa- tions of motion mx" = -2kx + ky, ту" — kx – 2k y + kz, mz" ky – 2kz. Assume that m = k = 1. Show that the natural fre- quencies of oscillation of the system are w1 = v2, w2 = y2- v2, and w3 = V2+ /2. WwwwwWM m w m Www m kwM FIGURE 4.2.7. The mechanical system of Problem 47.
Solve this ? For the system shown in Fig. 4.2.7, derive the equa- tions of motion mx" = -2kx + ky, ту" — kx – 2k y + kz, mz" ky – 2kz. Assume that m = k = 1. Show that the natural fre- quencies of oscillation of the system are w1 = v2, w2 = y2- v2, and w3 = V2+ /2. WwwwwWM m w m Www m kwM FIGURE 4.2.7. The mechanical system of Problem 47.
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Transcribed Image Text:Solve this ?
For the system shown in Fig. 4.2.7, derive the equa-
tions of motion
mx" = -2kx + ky,
ту" —
kx – 2k y + kz,
mz"
ky – 2kz.
Assume that m = k = 1. Show that the natural fre-
quencies of oscillation of the system are
w1 = v2, w2 = y2- v2, and w3 = V2+ /2.
WwwwwWM m w m Www m kwM
FIGURE 4.2.7. The mechanical system of
Problem 47.
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