**Introduction**

In this experiment(Nonlinear Oscillations in Mechanical Systems), we will be studying the motion of a chaotic particle in a mechanical system by applying a nonlinear periodic force to it.

We know that in a simple mechanical system, the appearance of chaotic dynamics is a fundamental classical phenomenon.

**Aim**

To study the chaotic motion of a particle under a non-linear force in a mechanical system.

**Theory**

1. Collider is a kind of linear accelerator or ring accelerator that brings two moving particles in opposite directions together and makes them collide.

2. It is used in research to collide one particle with another by giving them high kinetic energy.

** A Collider**

**Requirements**

1. A computer

2. Notebook

3. A calculator

4. Pen or Pencil

**Procedure**

**Step 1:** With the help of computer modeling, stimulate a nonlinear oscillation.

**Step 2:** Treat this computer modeling as a sequence of matrix multiplication.

**Step 3:** Under external force, each of these matrices will be taken as the linear and nonlinear oscillations of a mechanical body.

**Step 4:** Record your observation of motion in a notebook.

**Observation**

1. After doing the matrix multiplication we obtained the chaotic motion performed by a particle.

2. The particle performs this motion under non-linear and linear forces.

**Result**

1. The motion that the particle performed in this experiment, is a type of beam-beam effect action.

2. This also limits the particle collide intensity.

**Precaution**

1. Record your observation carefully.

2. Solve matrix multiplication correctly.

**Conclusion**

In this experiment, we studied the motion of a particle inside a collider in the presence of linear and nonlinear forces.

**Viva Questions With Answers**

**Q.1 What was the aim of your experiment?**

ANS. To study the motion of particles under the linear and non-linear forces.

**Q.2 What do you understand about the beam-beam effect?**

ANS. It is a kind of limitation in particle colliders of high intensity. The deviation obtained in a beam when it crosses the other beam is termed the beam-beam effect.

An Indian nuclear physicist, founding director, and professor of physics at the Tata Institute of Fundamental Research.

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