Question

How does the Force change if the spring constant increases.

Answer 1

Explanation:

1. The restoring force will increase with an increase in the spring constant. As a result, the acceleration increases at each displacement point.

Spring Constant Definition:

1. Simple harmonic motion is an intriguing type of motion. It is often applied to things moving in oscillating motion. Springs often have SHM. Springs have "spring constants" built in that specify how rigid they are. A well-known law called Hooke's law gives an explanation of the SHM and a formula for the applied force using the spring constant.
2. We will examine the formula for Hooke's law to understand the concept of axiom constant. The spring constant formula is another name for Hooke's law. The equation is shown below.
3. Formula : $F=-KX$, Where F denotes the recoil force of the spring, x denotes the displacement of the spring, and k is referred to as the spring constant. The units of the spring constant are specified as newtons per meter.

The expression of the frequency of a spring-mass system:

Young's modulus of elasticity,

$$\begin{gathered} Y=\frac{Stress}{Strain} \\ Y=\frac{{\displaystyle \frac{F}{A}}}{{\displaystyle \frac{∆L}{L}}} \end{gathered}$$
Here,

$F=$Force needed to extend or compress the spring

$A=$Area over which the force is applied

$L=$Nominal length of the material

$\Delta L=$change in the length

$$\begin{gathered} \frac{Y∆L}{L}=\frac{F}{A} \\ F=\frac{YA}{L}\left(∆L\right) \end{gathered}$$
Here,

$$\begin{gathered} K=\frac{YA}{L} \\ \Rightarrow K\propto \frac{1}{L} \end{gathered}$$
Therefore, the above equation can be written as

$\Rightarrow F=Kx$

Observe that, $F$ is directly proportional to $K$. So as the constant increases the force also increases.