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(1I) Consider two objects, A and B, both undergoing SHM, but with different frequencies, as described by the equations $x_{\mathrm{A}}=(2.0 \mathrm{m}) \sin (2.0 t)$ and $x_{\mathrm{B}}=(5.0 \mathrm{m}) \sin (3.0 t),$ where $t$ is in seconds. After $t=0,$ find the next three times $t$ at which both objects simultaneously pass through the origin.

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$$3.1 \mathrm{s}, 6.3 \mathrm{s}, 9.4 \mathrm{s}$$

05:28

Shital Rijal

Physics 101 Mechanics

Chapter 14

Oscillators

Motion Along a Straight Line

Motion in 2d or 3d

Periodic Motion

University of Michigan - Ann Arbor

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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Consider two objects, A an…

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The displacement $d$ (in m…

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Two waves are described by…

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Three simple harmonic moti…

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Refer to the equations in …

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In SHM, the distance of pa…

03:41

(II) Figure $11-50$ shows …

01:10

03:40

1. Object Undergoing SHM A…

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00:37

07:32

The displacement of a part…

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12. A Body Oscillates A bo…

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Two particles undergo SHM …

in this problem on the topic of oscillators, we are considering two objects A and B, both undergoing simple harmonic motion and both their equations of motion given after T. Is equal to zero seconds. We want to find the next three times at which both objects will simultaneously pass through the origin. Now each object will pass to the origin at the times when the argument of its science function is a multiple of pi. And so for object A two times T. A. Must equal to some multiple of pi will call in a times pi. This means that T. A. Is equal to a half times the integral multiple of pie and a. Hi! So remember any can be any Natural # 1, 2, 3 etcetera. And so this means that T. A. Can be half pie. Hi the over two pi two pi 5/2 pi three pi 7/2 pi four Pi and so on. Now, similarly for oscillated B Will be, we have three times T. B must equal to some integer multiple of pie and be times pi which means that T B Must equal to 1 3rd N. B. Times pi Where again, N. B. Is some natural number 123 etcetera. So T B then is 1 3rd times pi two thirds pie. Hi four thirds pi five thirds pie, two pi seven over three pi 8/3 pi, three pi etcetera. So we can see from here that the first three times at T is equal to hi seconds, two pi seconds And three pi seconds which is simply 3.1 seconds, 6.3 seconds And 9.4 seconds.

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