Springs in series and parallel

Article about the 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

F_s = F₁ = F₂

3. The equivalent spring’s constant (k_s)

1/k_s = 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

If 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

F_s = F₁ + F₂

3. The equivalent spring’s constant (k_p)

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 (k_p) = c + c = 2c