In the three-railway-car system of Fig. 5.4.6, suppose that cars 1 and 3 each weigh 32 tons, that car 2 weighs 8 tons, and that each spring constant is 4 tons/ft. If x (0) = vo and x, (0) = x, (0) = 0, show that the two springs are com- pressed until t = 1/2 and that x{() = -}vo and x() = x,(t) = +gvo thereafter. Thus car 1 rebounds, but cars 2 and 3 continue with the same velocity. k2 k3 тy т, тз 00.00o0.0o To0.00 FIGURE 5.4.6. The three railway cars of Example 2.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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In the three-railway-car system of Fig. 5.4.6, suppose that
cars 1 and 3 each weigh 32 tons, that car 2 weighs 8 tons,
and that each spring constant is 4 tons/ft. If x (0) = vo
and x, (0) = x, (0) = 0, show that the two springs are com-
pressed until t = 1/2 and that
x{() = -}vo and x() = x,(t) = +gvo
thereafter. Thus car 1 rebounds, but cars 2 and 3 continue
with the same velocity.
k2
k3
тy
т,
тз
00.00o0.0o
To0.00
FIGURE 5.4.6. The three railway
cars of Example 2.
Transcribed Image Text:In the three-railway-car system of Fig. 5.4.6, suppose that cars 1 and 3 each weigh 32 tons, that car 2 weighs 8 tons, and that each spring constant is 4 tons/ft. If x (0) = vo and x, (0) = x, (0) = 0, show that the two springs are com- pressed until t = 1/2 and that x{() = -}vo and x() = x,(t) = +gvo thereafter. Thus car 1 rebounds, but cars 2 and 3 continue with the same velocity. k2 k3 тy т, тз 00.00o0.0o To0.00 FIGURE 5.4.6. The three railway cars of Example 2.
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