Simple Harmonic Motion (Shm)

Simple Harmonic Motion (SHM) is an oscillatory motion characterized by a restoring force proportional to displacement from equilibrium.

What Is Simple Harmonic Motion?

Simple Harmonic Motion (SHM) is an oscillatory motion where the restoring force is proportional to the displacement from an equilibrium position.

Equation Of Shm

This section explores the equation of Simple Harmonic Motion (SHM) and its derivation from Newton's second law.

General Solution To Shm

This section discusses the general solution to Simple Harmonic Motion (SHM) and its key components, including amplitude, angular frequency, and phase constant.

Physical Quantities In Shm

This section explores the fundamental physical quantities associated with Simple Harmonic Motion (SHM), including velocity, acceleration, and energy.

Mechanical And Electrical Shm

This section discusses the principles of Simple Harmonic Motion (SHM) in both mechanical and electrical systems, emphasizing the similarities and governing equations.

Mechanical Shm – Mass-Spring System

This section introduces mechanical simple harmonic motion (SHM) through the mass-spring system, discussing key relationships between force, motion, and energy.

Electrical Shm – Lc Oscillator

This section introduces the concept of Electrical Simple Harmonic Motion through the study of LC oscillators and their equations.

Analogy Table

The analogy table illustrates the similarities between mechanical and electrical simple harmonic motion (SHM) across various parameters.

Why Study Electrical Oscillators?

Electrical oscillators are fundamental components in various electrical systems, playing a crucial role in communication and signal processing.

Complex Number Notation & Phasor Representation Of Shm

This section explores how complex numbers simplify the mathematics of simple harmonic motion (SHM) and introduces phasor representation.

Why Use Complex Numbers In Shm?

Complex numbers are utilized in simple harmonic motion to simplify calculations, particularly with multiple oscillators, damping, and forced oscillations.

Complex Representation Of Shm

Complex representation of SHM utilizes complex numbers to simplify the understanding of oscillatory motion.

Phasor Representation

Phasors are rotating vectors used to simplify the analysis of oscillatory systems in physics, particularly in simple harmonic motion (SHM).

Damped Harmonic Oscillator

Damped harmonic oscillators are systems where the amplitude of oscillation decreases over time due to energy losses from damping forces.

Damping – Introduction

Damping refers to the decrease in amplitude of oscillations in real systems due to energy loss from friction or resistance.

Types Of Damping

This section covers the different types of damping in oscillatory systems, highlighting how damping affects motion and energy.

Energy Decay

In this section, we explore energy decay in damped harmonic oscillators, focusing on how total energy decreases over time due to damping forces.

Quality Factor Q

The Quality Factor Q measures the underdamped nature of an oscillator, affecting how quickly it loses energy and the sharpness of resonance.

Forced Oscillations

Forced oscillations occur when an external periodic force influences a system, leading it to oscillate at the force's frequency.

Introduction

This section introduces students to the foundational concepts of Simple Harmonic Motion (SHM), including its definition, important equations, and physical quantities involved.

General Solution

The general solution to forced oscillations encompasses both transient and steady-state solutions, highlighting their distinct behaviors.

Steady-State Solution

The steady-state solution describes the response of a forced oscillator after any transient behaviors have diminished, focusing on the system's behavior at the driving frequency.

Resonance

Resonance occurs when an external oscillation frequency matches the system's natural frequency, resulting in maximum amplitude.

Electrical Analogy — Forced Rlc Circuit

This section discusses the electrical analogies of mechanical forced oscillators, focusing on RLC circuits and their similarities to mechanical systems.

Impedance

Impedance is a key concept in both electrical and mechanical oscillatory systems, representing the overall resistance to motion due to damping and stiffness/inductance.

Power Absorption

This section explores the concepts of instantaneous power, average power, and power absorption in simple harmonic motion (SHM), especially at resonance.

Instantaneous Power

This section discusses the concept of instantaneous power in oscillatory systems and its relation to the forces acting on the system.

Average Power

This section discusses average power in the context of steady-state forced simple harmonic motion, emphasizing how it can be calculated and its behavior at resonance.

Power At Resonance

Power absorption in a forced oscillation system reaches its peak at resonance, where the driving frequency matches the natural frequency of the system.

Summary

This section encapsulates the essential concepts of Simple Harmonic Motion (SHM) and its significance in mechanical and electrical systems, alongside insights into damping, forced oscillations, and resonance.