**Simple Harmonic Oscillator: A 0.100 kg Mass in Motion**

**Introduction**

A simple harmonic oscillator (SHO) is a fundamental concept in physics that describes the motion of an object that oscillates about a fixed point. In this article, we will explore the characteristics of a SHO with a mass of 0.100 kg.

**What is a Simple Harmonic Oscillator?**

A simple harmonic oscillator is a type of oscillatory motion that occurs when an object is displaced from its equilibrium position and then returns to it, repeating the process in a regular and periodic manner. The SHO is characterized by a constant force that is proportional to the displacement of the object from its equilibrium position.

### Mathematical Representation

The motion of a SHO can be represented mathematically using the following equation:

**F = -kx**

Where:

- F is the force acting on the object
- k is the spring constant
- x is the displacement of the object from its equilibrium position

**Characteristics of a 0.100 kg SHO**

### Frequency and Period

The frequency (f) of a SHO is given by the following equation:

**f = (1/2π) * √(k/m)**

Where:

- m is the mass of the object (0.100 kg in this case)

The period (T) of the SHO is the time taken by the object to complete one oscillation and is given by:

**T = 1/f**

### Amplitude and Phase

The amplitude (A) of a SHO is the maximum displacement of the object from its equilibrium position. The phase (φ) of the SHO is the initial displacement of the object from its equilibrium position.

### Energy

The total energy (E) of a SHO is the sum of the kinetic energy (K) and potential energy (U) of the object:

**E = K + U**

Where:

- K = (1/2) * m * v^2
- U = (1/2) * k * x^2

### Example Problem

Suppose a 0.100 kg mass is attached to a spring with a spring constant of 10 N/m. If the mass is displaced by 0.05 m from its equilibrium position, what is its speed when it passes through the equilibrium position?

**Solution:**

First, we need to find the frequency of the SHO:

**f = (1/2π) * √(10 N/m / 0.100 kg) = 1.58 Hz**

Next, we need to find the amplitude of the SHO:

**A = 0.05 m**

Finally, we can find the speed of the mass when it passes through the equilibrium position:

**v = A * 2πf = 0.05 m * 2π * 1.58 Hz = 0.49 m/s**

**Conclusion**

In conclusion, a simple harmonic oscillator with a mass of 0.100 kg is a fundamental system that exhibits periodic motion. By understanding the characteristics of a SHO, we can analyze and predict the motion of objects in a wide range of physical systems.