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. Alfredo D. Bobadilla. An element of the electrical circuit experiences movement or oscillations.. Notice how the electrical current depends on the capacitor displacement.. In the system shown, the electrical behavior depends on mechanical properties.. AP Calculus BC. Nonhomogeneous Differential Equations. Recall that second order linear differential equations with constant coefficients have the form:. Now we will solve equations where . G. (. x. ) . 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. 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:. Outline. Oscillators. Inverter-Based Oscillator. Introduction of Phase Noise Simulation. LC-Tank Based Oscillator. Laplace Analysis. Circuit Implementation. Quality Factor Analysis. Inverter-Based Oscillator.  . 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. Syllabus. Winter 2018. Instructor and Textbook. Instructor: Roxin Zhang. Class: MWF 12:00 – 12:50 pm, . Jamrich. 3315. Office Hours: MWRT 11-11:50 am, . Jamrich. 2208. Text: A First Course in Differential Equations, 11th . MA361 Differential Equations Syllabus Winter 2018 Instructor and Textbook Instructor: Roxin Zhang Class: MWF 12:00 – 12:50 pm, Jamrich 3315 Office Hours: MWRT 11-11:50 am, Jamrich 2208 Text: A First Course in Differential Equations, 11th 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. Quick example. How to solve differential equations. Second example. Some questions. How many tons of fish can fishermen harvest from a lake each year without endangering the fish population?. Some questions. Vector algebra. Scalar and vector fields. Differential calculus: Gradient, divergence, curl. Integral calculus: Line integrals, surface integrals, volume integrals. Basic theorems: Divergence, Stokes.