Problem_05_01 - Problem 5.1 Given A third spring of...

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Problem 5.1 Given: A third spring of constant k 3 and a weight W 3 are added to the system of Example 5.3. Find: Displacements q 1 , q 2 , and q 3 Solution: We will use a somewhat different approach than example 5.3 For a sigle spring, the strain energy is: U 1 2 k δ 2 = Eq. 5.12 where δ is the stretch of the spring. The force in the spring is: Nk δ = or δ 2 N k 2 = Thus: U 1 2 N 2 k = For the three springs, the strain energy is: U 1 2 N 1 2 k 1 1 2 N 2 2 k 2 + 1 2 N 3 2 k 3 + = N 1 W 1 W 2 + W 3 + = N 2 W 2 W 3 + = N 3 W 3 = U 1 2 W 1 W 2 + W 3 + () 2 k 1 1 2 W 2 W 3 + 2 k 2 + 1 2 W 3 2 k 3 + = q 1 W 1 1 2 W 1 W 2 + W 3 + 2 k 1 1 2 W 2 W 3 + 2 k 2 + 1 2 W 3 2 k 3 + d d = q 1 2W 1 2 + 3 + 2k 1 = q 2 W 2 1 2 W
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