As we will study in the coming weeks, the one-dimensional motion of a mass attached to a spring without friction is governed by the linear second-order equation with constant coeffi- cients (1) d²x dt² +w²x = 0, where w² is a positive parameter. (a) Find the general solution to equation (1). You should have found a periodic solution: can you say what the period is? (b) Find the particular solution assuming that the mass is initially still in position to at t = 0, i.e., using the initial conditions x(0) = xo and d (0) = 0. (c) With friction, the motion is described by the equation d²x dt² dx + f +w²x = 0, dt where both f and w² are positive parameters. Find the general solution to equation (2) and sketch the behaviour of the solution in time (remember to discuss all the possible cases!). Is this a periodic function? If so, can you find the period?

As we will study in the coming weeks, the one-dimensional motion of a mass attached to a spring without friction is governed by the linear second-order equation with constant coeffi- cients (1) d²x dt² +w²x = 0, where w² is a positive parameter. (a) Find the general solution to equation (1). You should have found a periodic solution: can you say what the period is? (b) Find the particular solution assuming that the mass is initially still in position to at t = 0, i.e., using the initial conditions x(0) = xo and d (0) = 0. (c) With friction, the motion is described by the equation d²x dt² dx + f +w²x = 0, dt where both f and w² are positive parameters. Find the general solution to equation (2) and sketch the behaviour of the solution in time (remember to discuss all the possible cases!). Is this a periodic function? If so, can you find the period?

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.2: Introduction To Conics: parabolas

Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

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