# Spring Force Formula

## Spring Force Formula

When an object’s motion repeats with a defined cycle, it is said to be in periodic motion. This motion is also known as oscillation. Simple examples include the movement of springs and pendulums, but oscillations can occur in a variety of other situations. The object has a stable equilibrium position, which is an important feature of periodic motion. A restoring force is also directed toward that position. Force is applied by a spring. With examples, this topic will explain the spring force concept and Spring Force Formula.

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### Concept of Spring Force

There is a position in which the springs are at rest. When they are stretched or compressed, however, a restoring force exists that always points in the direction of the equilibrium position. Pendulums are stable when hanging straight down. When a pendulum is pulled away from its equilibrium position, it swings back and forth as tension force and gravity act on it.

Spring is a common tool, and their inertia is frequently overlooked due to their negligible mass. When a spring is strained, it will undergo displacement; when it is compacted, it will become compressed. Then it reaches its equilibrium point. As a result, a spring exerts an equal and opposite force on a body that compresses or stretches it.

Consider a spring with one end attached to a hook and the other attached to an object with mass m and allowed to hang down vertically. In this case, the object will be subject to two forces. One force will be the spring’s restoring force, which will be directed upward. The other force will be gravity acting on the mass in a downward direction. If the mass is not moving, it will remain at rest in an equilibrium position with a zero net force.

### The Formula for Spring Force

Simple Harmonic Periodic motion encompasses motion. In SHM, the restoring force Fx is proportional to the displacement x. This restoring force and displacement always have opposing signs. The force equation can be formed using a proportionality constant k.

i.e. Fx = – k x

For springs, this relationship is Hooke’s Law, where k will be the spring constant. The SI unit of k is Newton per meter,

In another form, F=k(x–x0)

Where,

x the displacement of the spring from its equilibrium position

k the spring constant

F spring force

xo equilibrium position

### Solved Examples for Spring Force Formula

Q.1: A spring has a length of 22 cm per s. If it is loaded with 2 kg weight, then it gets stretched by 38 cm per sec. Determine its spring constant using Spring Force Formula.

Solution: Known parameters are,

(Mass) m = 2 kg,

(initial length) xo = 22 cm,

(displacement) x = 38 cm

Final displacement = x–xo=38cm–22cm=16cm = 0.16 m

The spring force will be,

F = ma  (Newton’s law)

= 2 kg × 0.16 m

= 0.32 N

The spring constant,

K=–Fx−x0

= – 0.320.16

= – 2 N per m

Thus, the spring constant will be – 2 N per m.

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