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(II) If one oscillation has 5.0 times the energy of a second one of equal frequency and mass, what is the ratio of their amplitudes?

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$$A_{1} : A_{2}=\sqrt{5} : 1$$

02:28

Shital Rijal

Physics 101 Mechanics

Chapter 14

Oscillators

Motion Along a Straight Line

Motion in 2d or 3d

Periodic Motion

Cornell University

University of Washington

Simon Fraser University

Hope College

Lectures

04:01

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.

02:18

In physics, an oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. The oscillation may be periodic or aperiodic.

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for this problem on the topic of oscillators, we are told that one oscillating mass has five times the energy of a second one but has but both have the same frequency and mess. And we want to know the ratio of the amplitudes to compare the total energies, we can compare the maximum potential energies. And since the frequencies and masses are the same, the spring constants are the same. So the energy of the high energy isolation over the energy of the low energy oscillation will use E. H. And L. For these respectively is equal to a half. Okay, A edge squared over a half. A K A L squared OK. Is the same in both circumstances. So we can see the harvey's cancel and so to do the case. So we left with a squared H over a squared out and we know the ratio of the energies is five. So a squared H over a squared L. Is also equal to five, which means the ratio of the amplitude for the high energy oscillation over the amplitude of the low energy oscillation. Edge of a L. Is simply the square root of five.

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