# SHM, Determing Spring Constant from Period^2 vs. Mass

• nmacholl
In summary, SHM stands for Simple Harmonic Motion and is a periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position. The spring constant can be determined by plotting the period<sup>2</sup> against the mass of an object undergoing SHM, with the slope of the graph equal to 4π<sup>2</sup>/k. In SHM, the period<sup>2</sup> is directly proportional to the mass, expressed as T<sup>2</sup> ∝ m. The spring constant is a characteristic of a specific spring and does not change in SHM, but the effective spring constant may change if the spring is stretched or compressed beyond its elastic limit.

#### nmacholl

Help!

I'm trying to find the spring constant (k) of a spring using simple harmonic motion. I have a graph of Period^2 vs. Mass.

Knowing that T=2*$$\pi$$*$$\sqrt{m/k}$$

How would one find k from the slope of this graph?
My linear fit yields: y=5.237x+0.003
5.237 being my slope

HINT: Using what you know can you get an Equations for T^2 in terms of mass? If so, the slope of that equation is 5.237.

To find the spring constant from the slope of the graph, we can use the equation T=2*\pi*\sqrt{m/k}. By rearranging this equation, we can see that the slope of the graph (5.237) is equal to 2*\pi/\sqrt{k}. This means that we can calculate the spring constant by taking the reciprocal of the slope and squaring it, giving us k = (2*\pi/5.237)^2 = 0.736 N/m (assuming the units for period are in seconds and mass in kilograms). This method works because the slope of the graph represents 2*\pi/\sqrt{k}, which is the relationship between the period and the spring constant. So, by calculating the slope and using the equation, we can determine the spring constant from the graph.

## 1. What is SHM?

SHM stands for Simple Harmonic Motion. It is a type of periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position.

## 2. How is the spring constant determined from period2 vs. mass?

The spring constant can be determined by plotting the period2 against the mass of an object attached to a spring undergoing SHM. The slope of the graph is equal to 4π2/k, where k is the spring constant.

## 3. What is the relationship between period2 and mass in SHM?

In SHM, the period2 is directly proportional to the mass. This means that as the mass increases, the period2 also increases. This relationship can be expressed as T2 ∝ m, where T is the period and m is the mass.

## 4. Can the spring constant change in SHM?

The spring constant is a characteristic of a specific spring and does not change in SHM. However, the effective spring constant may change if the spring is stretched or compressed beyond its elastic limit.

## 5. What is the importance of determining the spring constant in SHM?

Determining the spring constant is important because it allows us to predict the period of an object undergoing SHM and understand the behavior of the system. It also helps in designing and adjusting springs for various applications, such as in mechanical systems and instruments.