Difference between revisions of "Mechanics Qual Problems"

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1.) Whan a mass, <math>M</math>, is hung from the end of a spring of negligible mass it is found to undergo simple 1-dimensional harmonic motion with an angular frequency <math>\omega_o</math>
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1.) When a mass, <math>M</math>, is hung from the end of a spring of negligible mass it is found to undergo simple 1-dimensional harmonic motion with an angular frequency <math>\omega_o</math>.  The spring is then cut at its midpoint and the mass is reattached there.  The spring is then placed in a horizontal rough that allows <math>M</math> to move only in the <math>x</math> direction and the ends of the spring are fixed.  Here <math>x</math>, the coordinate of <math>M</math>, is measured from the equilibrium position of the midpoint of the spring.
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a.) Find, in terms of <math>\omega_o</math>, the angular frequency, <math>\omega_1</math>, of the oscillations of the mass <math>M</math> when it is displaced a small distance from equilibrium.  You may assume that the contact of the mass and spring with the wall of the trough is frictionless.

Latest revision as of 20:46, 22 August 2007

1.) When a mass, [math]M[/math], is hung from the end of a spring of negligible mass it is found to undergo simple 1-dimensional harmonic motion with an angular frequency [math]\omega_o[/math]. The spring is then cut at its midpoint and the mass is reattached there. The spring is then placed in a horizontal rough that allows [math]M[/math] to move only in the [math]x[/math] direction and the ends of the spring are fixed. Here [math]x[/math], the coordinate of [math]M[/math], is measured from the equilibrium position of the midpoint of the spring.

a.) Find, in terms of [math]\omega_o[/math], the angular frequency, [math]\omega_1[/math], of the oscillations of the mass [math]M[/math] when it is displaced a small distance from equilibrium. You may assume that the contact of the mass and spring with the wall of the trough is frictionless.