diff --git a/Lab05_Simple_Harmonic_Oscillator.ipynb b/Lab05_Simple_Harmonic_Oscillator.ipynb index 2261dc4..b2a74f1 100644 --- a/Lab05_Simple_Harmonic_Oscillator.ipynb +++ b/Lab05_Simple_Harmonic_Oscillator.ipynb @@ -23,9 +23,17 @@ "## Lab #5 - Simple Harmonic Oscillator \n", "### What are simple harmonic oscillators?\n", "\n", - "In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement. If restoring force is the only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes simple harmonic motion: sinusoidal oscillations about the equilibrium point, with a constant amplitude and a constant frequency (which does not depend on the amplitude).[\\[1\\]](https://en.wikipedia.org/wiki/Harmonic_oscillator)\n", + "In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium\n", + "position, experiences a restoring force proportional to the displacement. If restoring force is the\n", + "only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes\n", + "simple harmonic motion: sinusoidal oscillations about the equilibrium point, with a constant\n", + "amplitude and a constant frequency (which does not depend on the\n", + "amplitude).[\\[1\\]](https://en.wikipedia.org/wiki/Harmonic_oscillator)\n", "\n", - "Harmonic oscillators occur widely in nature and are exploited in many manmade devices, such as clocks and radio circuits. They are the source of virtually all sinusoidal vibrations and waves. In this lab, we will build spring-mass simple harmonic oscillator using common-place materials, and determine the stiffness of the spring based on governing equations of the system.\n" + "Harmonic oscillators occur widely in nature and are exploited in many manmade devices, such as\n", + "clocks and radio circuits. They are the source of virtually all sinusoidal vibrations and waves. In\n", + "this lab, we will build spring-mass simple harmonic oscillator using common materials, and\n", + "determine the stiffness of the spring based on governing equations of the system.\n" ] }, { @@ -34,13 +42,15 @@ "source": [ "### 1-DOF spring-mass system \n", "\n", - "Figure 1 shows the schematic of spring-mass simple harmonic oscillator. In this system with 1 mass and 1 spring, we have 1 degree of freedom. So, there is 1 differential\n", - "equations that describe the motion of mass. Employing Newton's law, $ F = ma = m \\ddot{x}$ and Hook's law for spring restoring forcce , $F = -kx$, to this sytem, the governing differential is obtained as: \n", + "Figure 1 shows the schematic of spring-mass simple harmonic oscillator. In this system with 1 mass\n", + "and 1 spring, we have 1 degree of freedom. So, there is 1 differential equation that describes the\n", + "motion of mass. Employing Newton's law, $ F = ma = m \\ddot{x}$ and Hook's law for spring restoring\n", + "force , $F = -kx$, to this sytem, the governing differential is obtained as: \n", "\n", "$m \\ddot{x} = -kx$ (1)\n", "\n", - "where $m$ and $k$ denote the mass and spring stiffness respectively. The differential\n", - "equations relate acceleration of mass $\\ddot{x}$ to displacement, $x$. \n", + "where $m$ and $k$ denote the mass and spring stiffness respectively. The differential equations\n", + "relate acceleration of mass $\\ddot{x}$ to displacement, $x$. \n", "\n", "\n", "