[[Force and Translational Dynamics]]

Spring force uses Hooke's law: $$\vec F_s=-k\Delta \vec x$$
$k$ = stiffness of spring
$\Delta x$ = displacement from measured from a relaxed length
negative sign means force points back towards equilibrium

Vertical spring stretched the spring until $k\Delta x = mg$ at equilibrium.

Hooke's law in magnitude is $|\vec F_s|=k|\Delta x|$
Spring constant k measures in N/m. Bigger k means more stiff (obviously).
Spring force is a restoring force that points towards equilibrium position of object spring relationship.
For a vertical spring with hanging mass, relaxed length is not equilibrium because gravity stretches spring

## Ideal Spring:
The mass of an ideal spring is treated as negligible compared to the objects attached to it.

- You can ignore the spring's own weight in calculations.
- You focus only on the interaction between the spring and the attached object.

An ideal spring follows a linear force-displacement relationship.

- The force is directly proportional to how far the spring is stretched or compressed.
- Stretch it twice as far and it pulls back with twice the force.
- This behavior stays consistent each time you use the spring.

## Direction of Spring Force
When a string is stretched:
* $\Delta x$ is positive
* Spring force is negative, pulling back
When a string is compressed:
* $\Delta x$ is negative
* Spring force is positive, pushing forward

WHEN CALCULATING THE $\Delta x$ OF A VERTICAL SPRING WITH A HANGING MASS, USE THE RELAXED POSITION NOT THE EQUILIBRIUM POSITION.