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I'm having some trouble understanding a multi-spring system.

Say I have 3 fixed nodes located at the following points in a 2D coordinate system:

node1: (2,4)

node2: (12,18)

node3: (30,6)

I have another node, node4, that is not fixed.

Then I connect node4 to all three fixed nodes using springs. The spring constants are as follows.

node4-node1: k1

node4-node2: k2

node4-node3: k3

My end goal is to determine the placement (coordinates) of node4, such that all the spring forces balance. i.e.

F_total = 0 = F1_4 + F2_4 + F3_4

How can I go about solving (or approximating) for the (x,y) coordinates of node4 such that the forces (or energy) of the system sums to zero?

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# Multi-spring system

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