Springs in series and parallel

1. Springs in series

If the spring is connected in series, as in the figure on the side, then:

1. The increase in the length of spring = the increase in length 1 + the increase in length 2

Δy = Δy1 + Δy1

2. The force experienced by equivalent spring = the force experienced by spring 1 = the force experienced by spring 2

Fs = F1 = F2

3. The equivalent spring’s constant (ks)

1/ks = 1/k1 + 1/k2

Sample problem 1:

Two identical springs each have a constant of 100 N / m connected in series. If the spring’s arrangement is given a load so that it increases 4 cm in length, then the increase in the length of each spring is …

Solution:

The total increase in the length of the two springs is 4 cm, therefore the increase in the length of each spring is 2 cm.

2. Springs in parallel

Springs in series and paralel 1If the spring is connected in parallel, as in the figure on the side, then:

1. The increase in the length of the equivalent spring = the increase in the length of spring 1 = the increase in the length of spring 2

Δy = Δy1 + Δy1

2. The force experienced by the equivalent spring = the force that is experienced by spring 1 + the force experienced by spring 2

Fs = F1 + F2

3. The equivalent spring’s constant (kp)

kp = k1 + k2

Sample problem 2:

Two springs each with constant c arranged in parallel. The spring constant of this arrangement becomes …

Solution:

The equivalent spring’s constant (kp) = c + c = 2c

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