bonus_1

bonus_1 - vector eld corresponding to the above equation...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
MEE 201 Advanced Dynamics. 10/16/2007. Bonus set No. 1 For extra credit, present 10/23/2007 in class. 1. Consider the following equation of motion for a mass-spring system: m ¨ x = kx - δx 3 . where m is the mass, k is the spring constant and δ is a positive constant representing the strength of the qubic nonlinearity. Write this as a dy- namical system in the phase space. Find the equilibrium points. Find the kinetic and potential energy. Show by an explicit calculation that the sum of the kinetic and potential energy is conserved during the motion. Can you solve the resulting system explicitly? Using MATLAB, plot the
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: vector eld corresponding to the above equation and, on the same plot, the contours of total energy of the system. Note how the vector eld is tangential to the contours of the energy. 2. A pendulum is acted upon by a torque T = a sin 2 ( ) where is the angle that the pendulum of mass m makes with the vertical axis and a is a constant. Write the second-order equations of motion using Newtons law. Represent the equations in phase-space form. Find the constant of motion. Plot the vector eld on the phase space on top of energy contours. 1...
View Full Document

This note was uploaded on 08/06/2010 for the course ME 201 taught by Professor Mezic,i during the Fall '08 term at UCSB.

Ask a homework question - tutors are online