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Engineering Mechanics

Engineering Mechanics. Instructor: Professor Manoj K Harbola, Department of Physics, IIT Kanpur. In this course, we would be studying mechanical interaction between different bodies when they interact through the forces applied on each other. Topics covered in this course include Review of Newton's laws of motion and vector algebra; Equilibrium of bodies; Plane trusses; Friction; Properties of plane surfaces; Method of virtual work; Motion of particles; Momentum; Work and energy; Rotational kinematics and dynamics; Simple harmonic oscillator; and Motion in non-inertial frames. (from nptel.ac.in)

Lecture 82 - Expanding Potential Energy about the Equilibrium Point and the Corresponding Force

With this lecture we begin to learn about simple harmonic motion. To motivate why this is important, in this lecture, we first discuss why the simplest motion about a stable equilibrium point in general can be described well by simple harmonic motion. Thus we expand the potential energy of a particle about its equilibrium point and show that in a majority of cases, it can be taken to be varying quadratically as a function of displacement leading to a restoring force proportional to the displacement.


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Review of Newton's Laws of Motion and Vector Algebra
Lecture 01 - Introduction to Vectors
Lecture 02 - Addition and Subtraction of Vectors
Lecture 03 - Multiplying Vectors
Lecture 04 - Introduction to Vectors: Solved Examples I
Lecture 05 - Transformation of Vectors under Rotation
Lecture 06 - Vector Products and their Geometric Interpretation
Lecture 07 - Vector Product: Kronecker-Delta and Levi-Civita Symbols
Lecture 08 - Vector Product: Kronecker-Delta and Levi-Civita Symbols (cont.)
Lecture 09 - Introduction to Vectors: Solved Examples II
Equilibrium of Rigid Bodies
Lecture 10 - Equilibrium of Rigid Bodies - Forces and Torques
Lecture 11 - Calculating Torques and Couple Moments
Lecture 12 - Calculating Torques and Couple Moments (cont.)
Lecture 13 - Finding a Force and a Couple Equivalent to an Applied Force
Lecture 14 - Different Elements and Associated Forces and Torques
Lecture 15 - Different Elements and Associated Forces and Torques (cont.)
Lecture 16 - Solved Examples; Equilibrium of Bodies I
Lecture 17 - Solved Examples; Equilibrium of Bodies II
Lecture 18 - Forces in Different Geometric Configuration
Plane Trusses
Lecture 19 - Plane Trusses: Building a Truss
Lecture 20 - Plane Trusses: Calculating Forces in a Simple Truss and Different Types of Trusses
Lecture 21 - Plane Trusses: Calculating Forces in a Simple Truss by Method of Joints
Lecture 22 - Solved Examples for Calculating Forces in a Simple Truss by Method of Joints
Lecture 23 - Solved Examples for Calculating Forces in a Simple Truss by Method of Joints (cont.)
Lecture 24 - Plane Trusses: Method of Selection for Calculating Forces in a Simple Truss
Friction
Lecture 25 - Dry Friction: Introduction with an Example
Lecture 26 - Dry Friction: A Solved Example
Lecture 27 - Dry Friction: Dry Thrust Bearing and Belt Friction with Demonstration
Lecture 28 - Dry Friction: Screw Friction and Rolling Friction
Lecture 29 - Dry Friction: Solved Examples
Properties of Plane Surfaces
Lecture 30 - Properties of Plane Surfaces: First Moment and Centroid of an Area
Lecture 31 - Centroid of an Area Made by Joining Several Plane Surfaces
Lecture 32 - Centroid of a Distributed Force and its Relation with Centre of Gravity
Lecture 33 - Solved Examples of Calculation of First Moment and Centroid of Distributed Forces
Lecture 34 - Second Moment and Product of an Area and Radius of Gyration
Lecture 35 - Parallel Axis Transfer Theorem for Second Moment and Product of an Area
Lecture 36 - Transformation of Second Moment and Product of an Area under Rotation of Coordinate Axes
Lecture 37 - Second Moment and Product of an Area, Solved Examples
Method of Virtual Work
Lecture 38 - Degrees of Freedom, Constraints and Constraint Forces
Lecture 39 - Virtual Displacement, Virtual Work and Equilibrium Condition in Terms of Virtual Work
Lecture 40 - Method of Virtual Work: Solved Examples
Motion of Particles
Lecture 41 - Motion of a Particle in a Plane in terms of Planar Polar Coordinates
Lecture 42 - Planar Polar Coordinates: Solved Examples
Lecture 43 - Description of Motion in Cylindrical and Spherical Coordinate Systems
Lecture 44 - Using Planar Polar, Cylindrical and Spherical Coordinate Systems: Solved Examples
Lecture 45 - Motion with Constraints, Constraint Forces and Free Body Diagram
Lecture 46 - Motion with Constraints - Solved Examples
Lecture 47 - Motion with Constraints - Solved Examples (cont.)
Lecture 48 - Motion with Constraints - Solved Examples (cont.)
Momentum
Lecture 49 - Equation of Motion in terms of Linear Momentum and the Principle of Conservation of Linear Momentum
Lecture 50 - Linear Momentum and Centre of Mass
Lecture 51 - Momentum Transfer, Impulse and Force due to a Stream of Particles Hitting an Object
Lecture 52 - Momentum and the Variable Mass Problem
Lecture 53 - Linear Momentum - Solved Examples
Work and Energy
Lecture 54 - Work Energy Theorem; Conservative and Non-conservative Force Fields
Lecture 55 - Definition of Potential Energy for Conservative Forces; Total Mechanical Energy and the Principle of Conservation Energy
Lecture 56 - Work and Energy Two Solved Examples using Conservation Principles
Lecture 57 - Further Discussion on Potential Energy
Lecture 58 - Work and Energy - Solved Examples
Lecture 59 - Applying Conservation Principles to Solve a Collision Problem
Lecture 60 - Work and Energy - Solved Examples
Rigid Body Motion
Lecture 61 - Degrees of Freedom and Number of Variables Required to Describe Motion of a Rigid Body
Lecture 62 - Equation of Motion for a Single Particle in terms of Angular Momentum and Torque; Motion of a Conical Pendulum
Lecture 63 - Conservation of Angular Momentum; Angular Momentum for a Collection of Particles
Lecture 64 - Applying Angular Momentum Conservation, a Solved Example
Rigid Body Motion (Fixed Axis Rotation)
Lecture 65 - Some Demonstrations of Conservation of Angular Momentum about Fixed Axis
Lecture 66 - Some More Demonstrations and Related Problems
Lecture 67 - Kinetic Energy and Moment of Inertia for Fixed Axis Rotation and Some Solved Examples
Lecture 68 - Solved Examples for Calculating Moment of Inertia and Conservation of Angular Momentum
Lecture 69 - Rigid Body Motion: Fixed Axis Rotation - Solved Examples
Lecture 70 - Rotation and Translation with Axis Moving Parallel to Itself
Lecture 71 - Solved Examples for Rotation and Translation with Axis Moving Parallel to Itself
Rigid Body Dynamics
Lecture 72 - Some Demonstrations on General Motion of Rigid Bodies
Lecture 73 - Infinitesimal Angles as Vector Quantities and Change of a Vector when Rotated by an Infinitesimal Angle
Lecture 74 - Angular Velocity and the Rate of Change of a Rotating Vector; Relating Change in Angular Velocity to an Applied Torque
Lecture 75 - Relationship between Angular Momentum and Angular Velocity
Lecture 76 - Rigid Body Dynamics - Solved Examples
Lecture 77 - A Review of the Relation between Angular Momentum and Angular Velocity
Lecture 78 - Solved Examples for Calculating Rate of Change of Angular Momentum and Torque
Lecture 79 - Understanding Demonstrations Shown Earlier using Equation of Motion
Lecture 80 - Understanding Demonstrations Shown Earlier using Equation of Motion: Euler Equations
Lecture 81 - Euler Equations, Solved Examples
Simple Harmonic Oscillator
Lecture 82 - Expanding Potential Energy about the Equilibrium Point and the Corresponding Force
Lecture 83 - Solving the Equation of Motion with Given Initial Conditions
Lecture 84 - Simple Harmonic Oscillator - Solved Examples
Lecture 85 - Representing Simple Harmonic Motion on a Phasor Diagram; Energy of an Oscillator
Lecture 86 - Simple Harmonic Oscillator - Solved Examples
Lecture 87 - Solving the Equation of the Motion with Constant Friction in the System
Lecture 88 - Harmonic Oscillator with Velocity-Dependent Damping (Heavy Damping)
Lecture 89 - Harmonic Oscillator with Velocity-Dependent Damping (Critical Damping)
Lecture 90 - Simple Harmonic Oscillator - Solved Examples
Lecture 91 - Harmonic Oscillator with Velocity-Dependent Damping (Light Damping)
Lecture 92 - Simple Harmonic Oscillator - Solved Examples (Light Damping)
Lecture 93 - Oscillations of an Undamped Harmonic Oscillator Subjected to an Oscillatory Force
Lecture 94 - Oscillations of a Forced Damped Harmonic Oscillator
Lecture 95 - Oscillations of a Forced Damped Harmonic Oscillator (cont.)
Lecture 96 - Energy and Power in a Forced Damped Harmonic Oscillator
Lecture 97 - Solved Examples (Forced Damped Harmonic Oscillator)
Motion in Non-inertial Frames
Lecture 98 - Equation of Motion in a Uniformly Accelerating Frame
Lecture 99 - Equation of Motion in a Uniformly Accelerating Frame; Solved Examples I
Lecture 100 - Equation of Motion in a Uniformly Accelerating Frame; Solved Examples II