- #1
mintsnapple
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Homework Statement
Homework Equations
f_spring = k(x_near - x_far)
The Attempt at a Solution
a. FBD:
The force goes through the nodes, and the sum of the forces must be 0 because the nodes are massless. Therefore, kx_1 = x(t)
So x_1(t) = x(t)/k
b. FBD:
For this system, the parallel springs have a k_eq of k + 2k + 3k = 6k. This is in series with the 5k spring, so the k_eq for both is 1/k_eq = 1/5k + 1/6k
= 5/30k + 6/30k
=11/30k
So k_eq = 30k/11.
Therefore, 30k/11(x_3 – x_1) = x(t)
So x_3(t) – x_1(t) = 11x(t)/(30k)
c. FBD:
Since the k_eq = 2k + 3k +k = 6k,
6k(x_2 – x_1) = x(t)
So x_2(t) – x_1(t) = x(t)/(6k)
Is my way of thinking correct?