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We 0 and k 0 The Damped Harmonic Oscillator The undamped b 0 system has equation mx kx 0 At this point you should have memorized the solution and also be able to solve oots Th. Natural frequency and damping ratio Well consider the second order homogeneous linear constant coe57358 cient ODE bx cx with positive spring constantmass In the absence of damping term this spring constant wo 00 10 m s 1 gravitational constant G 6673 10 11 N m kg 2 orbital constant G M 3986 10 14 m s 2 standard gravitational acceleration g 981 m s 1 Plancks constant h 6626 10 34 J s Boltzmanns constant k 1381 10 23 J K 1 first radiation constant c 1191 10 3. Applications of Newton’s Laws in 1 dimension. Free Fall. Motion in a Fluid. Spring motion. Molecular Dynamics. Free fall. Acceleration = g = 9.8 m/s. 2. = constant. Constant acceleration implies constant force = weight. Many natural (physical) phenomena exhibit . variation. = one quantity (quantities) changing on account of another (or several) . Principle is some kind of dependence. What things can we think about that depend on another action/object? . Applied Geophysics. 20 . Jan . 2016. © A.R. Lowry . 2016. Last time:. . Brief Intro to . Seismology . & . derivation of . the . Seismic Wave Equation. :. Four types of seismic waves:. . 5.2 MECHANICAL ENERGY. ENERGY = . ability to do . WORK. ENERGY = . ability to do . WORK. the energy of an object that . is due . to the object’s motion. KINETIC. POTENTIAL. the energy associated with . Review 2: Units 1-11. Mechanics Review 2 , Slide . 1. . Second Midterm. Friday. , . October 7. Important Formulas. Mechanics Review 2 , Slide . 2. Work of a Force: . Conservation of Energy:. Work-Kinetic Energy Theorem:. Periodic Motion – any repeated motion with regular time intervals. Simple Harmonic Motion – vibration about an equilibrium position in which a restoring force is proportional to the displacement from equilibrium . Engineering: B.4, pages 582-588. Free Vibration. A mass is free to oscillate. No external forces acting on the mass. Amplitude, frequency, period…all constant. Natural Frequency (. f. 0. ). The frequency of the free vibrations of a system. amplitude. ). . At which position is the magnitude of the acceleration of the mass maximum? . 0 B) M C) E D) . a is constant . everywhere. Clicker Question. Room Frequency BA. Acceleration = (. Introduction. Most mechanical devices such as fans, pumps, etc. produce vibration.. Vibration is easily transmitted through solid materials and may ‘appear’ elsewhere producing troublesome vibration and/or noise.. Formulated as Cauchy Problems. Ricky Bartels. . Back to Basics . The modeling of more complex spring-mass systems (such as a system of n masses and n 1 springs under the influence of friction) builds upon the model of the following system you probably recognize from differential equations. . Physics Oscillation 2.0 Practice Problem: A mass of 2 kg oscillating on a spring with constant 4 N/m passes through its equilibrium point with a velocity of 8 m/s. What is the energy of the system at this point? From your answer derive the maximum displacement,  For an isolated system, energy can be transformed to different forms, but cannot be created or destroyed.. Interesting idea. https://www.youtube.com/watch?v=PplaBASQ_3M. isolated system. A. . system of .