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Pr1. A metal rod having a mass m and length { has resistance R. The rod hangs from two vertical metallic wires of length l in a uni- form vertical magnetic field B of a horseshoe magnet (see figure). The wires have negligib- le resistance. An AC voltage source is connec- ted between the wires which provides a voltage U(t) = Uo cos wt, where Uo and w are constants. U(t) a) Show that for small angular displacements p the motion of the rod can be described by the cquation U(t) = aö + Bộ + n8, and express the constants a, 3, y in terms of quantities m, l, B, R and the gravitational ac- celeration g. b) At a certain frequency w = wo the ampli- tude of the oscillations of the rod becomes large and the equation above does not describe the motion anymore. Estimate the frequency wo-

Pr1. A metal rod having a mass m and length { has resistance R. The rod hangs from two vertical metallic wires of length l in a uni- form vertical magnetic field B of a horseshoe magnet (see figure). The wires have negligib- le resistance. An AC voltage source is connec- ted between the wires which provides a voltage U(t) = Uo cos wt, where Uo and w are constants. U(t) a) Show that for small angular displacements p the motion of the rod can be described by the cquation U(t) = aö + Bộ + n8, and express the constants a, 3, y in terms of quantities m, l, B, R and the gravitational ac- celeration g. b) At a certain frequency w = wo the ampli- tude of the oscillations of the rod becomes large and the equation above does not describe the motion anymore. Estimate the frequency wo-

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Pr1. A metal rod having a mass m and length e has resistance R. The rod hangs from two vertical metallic wires of length l in a uni- form vertical magnetic field B of a horseshoe magnet (see figure). The wires have negligib- le resistance. An AC voltage source is connec- ted between the wires which provides a voltage U(t) = Uo cos wt, where Uo and w are constants. U(t) S m IN a) Show that for small angular displacements p the motion of the rod can be described by the cquation U (t) = aö + Bộ + VP, and express the constants a, 3, y in terms of quantities m, l, B, R and the gravitational ac- celeration g. b) At a certain frequency w = wo the ampli- tude of the oscillations of the rod becomes large and the equation above does not describe the motion anymore. Estimate the frequency wo.
Transcribed Image Text:Pr1. A metal rod having a mass m and length e has resistance R. The rod hangs from two vertical metallic wires of length l in a uni- form vertical magnetic field B of a horseshoe magnet (see figure). The wires have negligib- le resistance. An AC voltage source is connec- ted between the wires which provides a voltage U(t) = Uo cos wt, where Uo and w are constants. U(t) S m IN a) Show that for small angular displacements p the motion of the rod can be described by the cquation U (t) = aö + Bộ + VP, and express the constants a, 3, y in terms of quantities m, l, B, R and the gravitational ac- celeration g. b) At a certain frequency w = wo the ampli- tude of the oscillations of the rod becomes large and the equation above does not describe the motion anymore. Estimate the frequency wo.
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