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Determine the equivalent spring constant , keq of the system shown. Motion is constrained to be inn vertical direction only.If m=10 kg and k=100 N/mm what is the equilibrium position of m and the force in the spring 1.

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The equivalent spring constant, (Keq) is 3.4K. And 2.885mm is the equilibrium position of m and the force in spring 1.

What is the Spring constant?

The term "spring constant" refers to the proportional constant k. It gauges the stiffness of the spring. A spring exerts a force F = -kx in the direction of its equilibrium position when it is stretched or compressed to a length that differs by an amount x from its equilibrium length.

Calculation:

Given

K1 = K2 = K3 = K4 = K5 = K6 = K7 = K8 = K9 = K10 = K11 = Keq

Wherein K3, K4, K5 and K10 are in parallel

This Keq = K3 + K4 +K5 + K10

Keq = 4K

K1 and K7 are in series so Keq'= K/2

Keq' and K11 are in parallel Keq" = 3K/2

Keq" And K8 are in series = Keq"'= {(3K/2) * K}/ {(3K/2) + K} = 3K/5

4K and K6 are in series Keq""= 4K/5

Keq = (3K/5) + K + (4K/5) = 3.4K

Now,

m= 10kg and k = 100N/m

mg = Keq (x)

x = mg/Keq

x = 10 * 9.81/3.4

x = 2.885mm.

Hence, the equivalent spring constant, (Keq) is 3.4K. And 2.885mm is the equilibrium position of m and the force in spring 1.

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