Difference between revisions of "Mechanics Qual Problems"
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| − | 1.) | + | 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.) | + | 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, , 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 . 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 to move only in the direction and the ends of the spring are fixed. Here , the coordinate of , is measured from the equilibrium position of the midpoint of the spring.
a.) Find, in terms of , the angular frequency, , of the oscillations of the mass 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.