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(1I) The amplitude of a driven harmonic oscillator reaches a value of 23.7$F_{0} / k$ at a resonant frequency of 382 Hz. What is the $Q$ value of this system?

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$$23.7$$

02:59

Shital Rijal

Physics 101 Mechanics

Chapter 14

Oscillators

Motion Along a Straight Line

Motion in 2d or 3d

Periodic Motion

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Rutgers, The State University of New Jersey

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Lectures

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2D kinematics is the study of the movement of an object in two dimensions, usually in a Cartesian coordinate system. The study of the movement of an object in only one dimension is called 1D kinematics. The study of the movement of an object in three dimensions is called 3D kinematics.

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for this problem on the topic of oscillators, We are given the value of the amplitude for a driven harmonic oscillator to be 23.7, If not over K. which occurs at the resonant frequency of 382 Hz were asked and to calculate the quality factor q of the system. Now, if we apply the resonance condition that the angular frequency omega psi omega not and were given that the aptitude a not Is equal to 23 0.7 times the president frequency. If not divided by. Okay, and note that for this condition to be true, The value of 23.7 must have units of second squared. And so a note, he is also equal to if not divided by mm times the square root of omega squared minus omega, north squared, all squared less b squared omega squared over m squared. So if we evaluate this when we're at the President frequency at omega equal to omega not. This becomes if not divided by M. And the square root and the first term cancels since omega is equal to omega note. So this becomes the square root of b squared omega north squared divided by M squared. And so we can rewrite this as if not divided by mm. To be omega not over mm. And so with the manipulation, this becomes if not we leave enumerated the same dividers by him times be times omega nought squared over. Em omega not so we multiply the top and the bottom of the denominator by omega nought. And so this becomes if not divided by um omega not squared divided by the quality factor Q. And so this simply becomes Q times F. Not of a cave. And so we know this is equal to 23.7 times F. Not over. Okay. Which is the given condition, which means that the quality factor Q of the system is 23 0.7

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