PPT-Differential Equation of the Mechanical Oscillator

Prepared by Dr Rajesh Sharma Assistant Professor Dept of Physics PGGC11 Chandigarh Email drrajeshsharmaincom The Hooks law 1 Let there be a body of mass m attached to a spring Then according to the Newtons Second law of motion we have. By: Kelly Martin. Differential Equation. Mathematical equation that relates some function with its derivatives. Usually, the functions represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between those two. Prepared by;. Dr. Rajesh Sharma. Assistant Professor. Dept of Physics. P.G.G.C-11, Chandigarh. Email: drrajeshsharma@in.com. Electrical Oscillator. A circuit consisting of an inductance (. L. ) and capacitance (. Slope Fields. Differential Equations. Any equation involving a derivative is called a . differential equation. .. The solution to a differential is a family of curves that differ by a constant.. Example:.  . An order . differential equation has a . parameter family of solutions … or will it?.  . 0. 1. 2. 3. 4. 0. 0. 1. 2. 3. 4. 1. 1. 2. 3. 4. 0. 2. 2. 3. 4. 0. 1. 3. 3. 4. 0. 1. 2. 4. 4. 0. 1. 2. Introduction to ODEs and Slope Fields. An . ordinary differential equation (ODE). is an equation involving a function . and some of its derivatives . , . ,….  . For example:.  . This equation says that . Fields. By: Leslie Cade. 1. st. period. Differential Equations. A differential equation is an equation which involves a function and its derivative. There are two types of differential equations: . General solution: is when you solve in terms of y and there is a constant “C” in the problem. y = e. x. y = e. 4x. y = e. x^2. y = sec x. dy. = e. x . dx. dy. = 4e. 4x . dx. dy. = 2xe. x^2 . dx. dy. = . tanxsecx. . dx. Slope Fields and Euler’s Method. Lesson 6.1. Objectives. Students will be able to:. (iv)Correct substitution for the solution of the differential equation of thetype (,)dxgxydy where () is a homogeneous function of thedegree zero is =vy.(v)Number of arbitrary constants in the particu Differential Equations. In this class we will focus on solving ordinary differential equations that represent the physical processes we are interested in studying. With perhaps a few exceptions the most complicated differential equation we will look at will be second order, which means it will look something like. Lecture-18. . Differential . Equation of the first order and higher . degree. UG (B.Sc., Part-2). Dr. Md. . Ataur. . Rahman. Guest Faculty. Department of Mathematics. M. L. . Arya. , College, . Kasba. Order Differential Equations. Dr J Frost (jfrost@tiffin.kingston.sch.uk) . Last modified: . 7. th. . August 2015. Intro. We’ve already seen that differential . equations are equations which relate . Higher order linear differential Equation. UG (B.Sc., Part-2). Dr. Md. . Ataur. . Rahman. Guest Faculty. Department of Mathematics. M. L. . Arya. , College, . Kasba. PURNEA UNIVERSITY, PURNIA. Contents. L. aplace . Transform. UNIT – IV. UNIT- V. PARTIAL DIFFERENTIAL EQUATIONS OF SECOND ORDER INTRODUCTION: . . An . equation is said to be of order two, if it involves at least one of the differential coefficients . Vector algebra. Scalar and vector fields. Differential calculus: Gradient, divergence, curl. Integral calculus: Line integrals, surface integrals, volume integrals. Basic theorems: Divergence, Stokes.