Mechanics Qual Problems - Revision history

Oborn at 20:46, 22 August 2007

2007-08-22T20:46:04Z

Oborn at 20:45, 22 August 2007

2007-08-22T20:45:53Z

Oborn at 20:45, 22 August 2007

2007-08-22T20:45:45Z

Oborn at 20:42, 22 August 2007

2007-08-22T20:42:07Z

New page

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>

← Older revision		Revision as of 20:46, 22 August 2007
Line 1:		Line 1:
−	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>. 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.	+	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.		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.

← Older revision		Revision as of 20:45, 22 August 2007
Line 1:		Line 1:
	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>. 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.		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>. 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.) ~~Fing~~, 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.	+	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.

← Older revision		Revision as of 20:45, 22 August 2007
Line 1:		Line 1:
−	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>	+	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>. 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.) Fing, 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.