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TE ILHooke on a Hook Somewhere DEEP BELOW THE EARTH's surface, at an UNKNOWN displacement from the Earth's center, a particle of mass m is dangled from a long string, length L; the particle osciljatonalong a small arc according to the differential cquation d²e dt2 36 Here, 0 refers to an angular displacement measured from the vertical and t refers to time. The particle's mass is given by m = 3 kg. The length of the string is given by L =° 5 meters. Whencver the particle arrives at a location of 0 = (T/12) radians from the vertical, the particle has no instantaneous specd. On both sides of the vertical, that is, 0 = (T/12) radians is repeatedly observed to be a 'turning point' for the particle's periodic motion. i. Draw a clear FREE-BODY diagram of this particle at some arbitrary point during ocillation, making sure to label variables and constants described above ii. Approximating to three significant digits if necessary, what is the angular frequency of this oscillator on a string? iii. Approximating to three significant digits if necessary, how many cycles per second should we expect of this pendulum? iv. What is the particle's approximate SPEED at t = T/4 seconds? (for which T'stands for 'Period' of this pendulum). v. If your F-B-D (1, above) is correct, you should find it reasonable to believe that: Tigsin = ma Given this, show how angular frequency depends on both the length of the string and the free-fall acceleration constant due to gravity. lim( sint=0

TE ILHooke on a Hook Somewhere DEEP BELOW THE EARTH's surface, at an UNKNOWN displacement from the Earth's center, a particle of mass m is dangled from a long string, length L; the particle osciljatonalong a small arc according to the differential cquation d²e dt2 36 Here, 0 refers to an angular displacement measured from the vertical and t refers to time. The particle's mass is given by m = 3 kg. The length of the string is given by L =° 5 meters. Whencver the particle arrives at a location of 0 = (T/12) radians from the vertical, the particle has no instantaneous specd. On both sides of the vertical, that is, 0 = (T/12) radians is repeatedly observed to be a 'turning point' for the particle's periodic motion. i. Draw a clear FREE-BODY diagram of this particle at some arbitrary point during ocillation, making sure to label variables and constants described above ii. Approximating to three significant digits if necessary, what is the angular frequency of this oscillator on a string? iii. Approximating to three significant digits if necessary, how many cycles per second should we expect of this pendulum? iv. What is the particle's approximate SPEED at t = T/4 seconds? (for which T'stands for 'Period' of this pendulum). v. If your F-B-D (1, above) is correct, you should find it reasonable to believe that: Tigsin = ma Given this, show how angular frequency depends on both the length of the string and the free-fall acceleration constant due to gravity. lim( sint=0

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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ILHooke on a Hook Somewhere DEEP BELOW THE EARTH's surface, at an UNKNOWN displacement from the Earth's center, a particle of mass m is dangled from a long string, length L; the particle oscilļatonalong a small arc according to the differential equation d²0 dt2 36 Here, 0 refers to an angular displacement measured from the vertical and t refers to time. The particle's mass is given by m = 3 kg. The length of the string is given by L =° 5 meters. Whenever the particle arrives at a location of 0 = (1/12) radians from the vertical, the particle has no instantaneous specd. On both sides of the vertical, that is, 0 = (T/12) radians is repeatedly obscrved to be a 'turning point for the particle's periodic motion. i. Draw a clear FREE-BODY diagram of this particle at some arbitrary point during oscillation, making sure to label variables and constants described above e ii. Approximating to three significant digits if necessary, what is the angular frequency of this oscillator on a string? iii. Approximating to three significant digits if necessary, how many cycles per second should we expect of this pendulum? iv. What is the particle's approximate SPEED at t = T/4 seconds? (for which T stands for 'Period' of this pendulum). v. If your F-B-D (i, above) is correct, you should find it reasonable to believe that: Nobe. Given this, show how angular frequency depends on both the length of the string and the free-fall acceleration constant due to gravity. B=fand lim(sint)=0
Transcribed Image Text:ILHooke on a Hook Somewhere DEEP BELOW THE EARTH's surface, at an UNKNOWN displacement from the Earth's center, a particle of mass m is dangled from a long string, length L; the particle oscilļatonalong a small arc according to the differential equation d²0 dt2 36 Here, 0 refers to an angular displacement measured from the vertical and t refers to time. The particle's mass is given by m = 3 kg. The length of the string is given by L =° 5 meters. Whenever the particle arrives at a location of 0 = (1/12) radians from the vertical, the particle has no instantaneous specd. On both sides of the vertical, that is, 0 = (T/12) radians is repeatedly obscrved to be a 'turning point for the particle's periodic motion. i. Draw a clear FREE-BODY diagram of this particle at some arbitrary point during oscillation, making sure to label variables and constants described above e ii. Approximating to three significant digits if necessary, what is the angular frequency of this oscillator on a string? iii. Approximating to three significant digits if necessary, how many cycles per second should we expect of this pendulum? iv. What is the particle's approximate SPEED at t = T/4 seconds? (for which T stands for 'Period' of this pendulum). v. If your F-B-D (i, above) is correct, you should find it reasonable to believe that: Nobe. Given this, show how angular frequency depends on both the length of the string and the free-fall acceleration constant due to gravity. B=fand lim(sint)=0
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