<p align="right">Last Update: <font color="#4f81bd">November, 26, 2024</font></p>
## BIG IDEAS
- A change in shape due to the application of a force is deformation.
- The size of the deformation is known as Hooke's law.
- The restoring force is directly proportional to the displacement of the mass.
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The [[Force|force]] exerted by a spring is a <font color="#f79646">restoring force</font>. [[Robert Hooke]] (1678) determined that the restoring force is directly proportional to the [[Displacement|displacement]] of the [[Mass|mass]].
![[Springs Hanging Vertically.png]]
### SI Unit
- The [[SI units]] for the spring constant is $N/m$
### Formula
$\vec{F}_s = -kx \tag{1}$,
where
$\vec{F}_s$ is the spring force,
$k$ is the spring constant, and
$x$ is the displacement of the spring.
- The negative sign is due to the restoring force being opposite the direction of the mass’s motion.
- The spring constant is a measure of the stiffness of a spring. A stiffer spring has a greater _k_ value.
### Background
- In the 1650s, Robert Hooke was working in Robert Boyle’s laboratory and studying elasticity.
- The law with his name states that a force is proportional (linear) to the distance stretching or compressing for certain elastic materials.
- The distance is the amount of deformation.
$\vec{F} \propto x$
- Adding a spring constant to the proportion changes this proportion to a simple equation:
$\vec{F} = -k x$
- where the $k$ is the spring constant, $x$ is the distance the material moves, and $\vec{F}$ is the restoring force.
- The minus sign designates the force acting in the direction opposite to the displacement.
- A force is a push or pull during an interaction between at least two objects.
- A newton is $kg \frac{m}{s^2}$
- Weight ($W$) is a force, where $W = m \cdot g$.
- The symbol $g$ represents the gravitational field strength.
- The numerical value of $g$ is based on the location of the object.
- Mass remains the same regardless of its location.
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==Simple Harmonic Motion== (SHM) is periodic motion from a _restoring force_ proportional to displacement.
> [!important]
> Simple harmonic motion describes the vibration of atoms, the variability of giant stars, and countless other systems from musical instruments to swaying.
Demonstration 1: Vibrating Spring
Demonstration 2: Equilibrium Position
The motion of Earth orbiting the sun is periodic. Is it simple harmonic motion? Why or why not?
#### Example Problem
What is the spring constant if a mass of 0.45 kg attached to a vertical spring stretches the spring 1.5 cm from its original equilibrium position?
#### Example Problem
What is the spring constant if a mass of 0.55 kg attached to a vertical spring stretches the spring 2.0 cm from the equilibrium position?
#### Example Problem
How much force is required to pull a spring 3.5 cm from its equilibrium position if the spring constant is 2.7 x10<sup>3</sup> N/m?
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### Related Topics
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