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Mutee Ur Rehman

Teaching with Labster

November 2, 2022

We will study the simple harmonic motion of spring and masses, hooke’s law, velocity, displacement, and other parameters of the mechanism of spring and masses. When we conduct any experiment, some factors, like air resistance, disturb the results. If we ignore air resistance, there will be ideal experimental conditions. There are various types of motions in physics. We are going to discuss Simple harmonic motion **(SHM)**. It is the simplest type of oscillation. Simple harmonic motion is when the restoring force of an object pushes the object toward its equilibrium position is equal to the displacement of object from its equilibrium position. The maximum distance between an object and its equilibrium position is called **amplitude (A).**

Equilibrium is an object's position where forces from all axes become zero.

In the above image, first, the length of the spring is its natural length. No force is acting. If we attach a mass, then the forces applying on the mass are the weight of mass and the reactive force of the table on mass. Both these forces cancel each other, and the effect of all forces becomes zero.

The most common example of the simple harmonic motion is the mass attached to a vertical ideal spring that obeys Hooke’s law. **Hooke’s law** states that for relatively small deformations, the displacement or size of deformation is a direct proportion of the weight or load of deforming object.

The equation of Hooke’s law is:

F* = *kx, where F is the force, x is a change in length, and k is the constant.* *

Hooke’s law is mostly obeyed in real-world cases. It is very effective for relatively short displacements.

Some parameters are measured during the spring and masses experiment.

**Frequency**: Frequency is denoted as “f” and it is the number of oscillations in one unit of time. Its unit is Hertz. Frequency is the reciprocal of the period of oscillations (T).**Period:**The period is the time taken by an object to complete the entire oscillation. Its unit is time (seconds).

Where M is the mass of the object and K is the spring constant.

Kinematic quantities are those that describe an object's motion, and they are displacement, velocity, and acceleration. As the time derivative of displacement,

**velocity**is the variation of position in time,**acceleration**is the variation of velocity in time, and**displacement**describes the position of the object at any given time (i.e. the time derivative of the velocity). When a mass oscillates with a vertical spring in simple harmonic motion, acceleration as a function of time has a sinusoidal pattern.There is also another force acting in simple harmonic motion which is Mechanical energy. It is the sum of kinetic and potential energy.

Earthquakes are often a cause of disturbance for the population. It is caused by the sudden breaking of rock within the earth which send some **seismic waves**. These waves usually shake or vibrate the ground. These waves are a result of sudden rush of energy in the earth’s sphere. These waves are recorded on seismographs. Two types of waves come. P (primary) and S (secondary) waves. **P-waves** are longitudinal waves and the fastest waves and arrive first at seismic stations. **S-waves** are transverse waves and are comparatively slower waves. The difference in arrival time between both waves represents the distance between the seismic station and the epicenter of the earthquake. The graph that forms on a seismogram with arrival of both waves is called **seismograph.** The time delay between both waves can be used to calculate the distance from the earthquake's epicenter and seismogram.

X=V.T

**The **earthquake's magnitude can be calculated by the distance of the epicenter and seismogram and the highest amplitude of the S-wave on the measuring scale.

Physics experiments are a little boring and lengthy for the students. In this topic, all concepts are connected to each other, and understanding all points is very important. Let’s discuss some reasons for the difficulty of spring and masses:

First of all, when studying this topic for the first time, it doesn't feel very easy. There are equations, graphs, and formulas that should be there for students to understand the topic fully. Formulas and equations are something that needs to be clarified in their application. Further, there is a concept of earthquakes and measurement of the magnitude of earthquakes which is a whole new concept for students. So, as a whole, this topic feels complicated and very vast.

There are definitions of each term that is related to the concept of spring and masses. Concept building is an important step in studying and learning a new topic. To read the definitions and understanding the concepts behind them can make students exhausted and less interested in the topic.

Without experimenting, it feels abstract to imagine results. The magnitude of an earthquake is calculated only by exact values of S-waves and epicenter distance. Thus it is very difficult for students to imagine the idea of earthquake measurement without visual illustration.

We have discussed the problems that may occur when students study this topic. So now it’s time to discuss some possible solutions to cope with the problems.

Revolutions are also made in every field. With each discovery, science steps towards advancement. In history, many scientists invented and discovered instruments that are useful sources for the conduction of many experiments. Let’s study some scientists who have prominent work in the field of masses and springs and its principles.

**Luigi Palmieri (1807-1896):**

He was an Italian physicist and meteorologist. He was renowned for his scientific research on Mount **Vesuvius eruptions**, earthquakes, and meteorological phenomena and for developing the era's seismograph. He received a degree in physics from the university of Naples.

He was appointed Chairman of Physics at the university in 1847 after being named Professor of Physics at the Royal Naval School in Naples in 1845. He started working at the Vesuvius Observatory in 1848, and in 1854 he was named the Observatory's Director. Palmieri could identify every minute motion while attempting to predict volcanic eruptions by using an electromagnetic seismometer to detect and measure ground tremors. He was also the first to discover helium on Earth in the lava of Mount Vesuvius.

One of the most effective methods to learn any topic is sharing knowledge and ideas between students. Students have different approaches to the same topic. While sharing their point of view, students discuss the main points of the topic and this discussion will eventually help them to clear their confusion. Some of the definitions which students must keep in mind during the discussion are:

Simple harmonic motion: it is the simplest type of motion of a mass attached to a vertical spring, which follows Hooke’s law.

**Hooke’s law:** It is stated that in displacements, the size of displacement is directly proportional to the load or displacing force.

**Equilibrium position:** The point where all the forces acting on a body becomes zero.

**Frequency:** The number of oscillations in one unit of time.

**Period:** The time taken by mass to complete the entire oscillation.

It is often observed that cramming doesn’t help much in science, especially in physics and mathematics. If you grab the logic instead of just read it and memorize, then you will never forget the key points. Understanding the mechanism of spring and masses is very important. Make diagrams and practice formulas and logically solve problems related to the topic. It will students to remember the topic with better logic.

As performance is very important in any experiment. We are reading things theoretically till now, and students must have developed the imagination and idea of spring and masses experiment and the seismographs in their minds. Now it’s time to see students' ideas into a picture that depicts the experiment more clearly.

A virtual lab is a great source of learning for students. At Labster, students can watch 3D simulations related to their topics. Students can also apply their knowledge on Labster. It’s about the experience of applying your knowledge and seeing the results.

Teachers monitor the activities of students. There is a scoring theme in Labster. Simulations are short and easy to watch. This platform help students gain confidence in their knowledge and encourage them to try more theories.

There are two 3D simulations related to springs and masses in Labster. The experiment with different springs and loads is conducted in both simulations. Also, it measures the epicenter of the earthquake and the distance of the epicenter from the seismogram by measuring the amplitude of S-waves.

Check out our two virtual labs:

__Springs and Masses (Principles): Learn how to detect and record earthquakes Virtual Lab__

__Springs and Masses: Learn how to detect and record earthquakes Virtual Lab__

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