The block is slowly pulled from its eqilibrium position to some position æinit > 0 along the x axis. At time t = 0, the block is released with zero initial velocity. The goal is to determine the position of the block x (t) as a function of time in terms of w and æini - It is known that a general solution for the displacement from equilibrium of a harmonic oscillator is æ(t) = C' cos (wt) + S sin (wt), where C, S, and w are constants. (Figure 2) Your task, therefore, is to determine the values of C and S in terms of w and rinit -
The block is slowly pulled from its eqilibrium position to some position æinit > 0 along the x axis. At time t = 0, the block is released with zero initial velocity. The goal is to determine the position of the block x (t) as a function of time in terms of w and æini - It is known that a general solution for the displacement from equilibrium of a harmonic oscillator is æ(t) = C' cos (wt) + S sin (wt), where C, S, and w are constants. (Figure 2) Your task, therefore, is to determine the values of C and S in terms of w and rinit -
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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Transcribed Image Text:Harmonic Oscillator Kinematics
2 of 22
The block is slowly pulled from its equilibrium position to
some position xịnit > 0 along the x axis. At time t = 0,
the block is released with zero initial velocity.
Constants I Periodic Table
The goal is to determine the position of the block x (t)
as a function of time in terms of w and xinit -
Part A
It is known that a general solution for the displacement
from equilibrium of a harmonic oscillator is
Using the general equation for x (t) given in the problem introduction, express the initial position of the block xinit
terms of C, S, and w (Greek letter omega).
in
x(t) = C cos (wt)+S sin (wt),
View Available Hint(s)
where C, S, and w are constants. (Figure 2)
Your task, therefore, is to determine the values of C and
S in terms of w and xinit -
Ηνα ΑΣφ
?
a
Figure
xa Xb
|X|
Х.10п
2 of 3
Tinit = C cos (wt)+S sin (wt)
+x
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x(1)
The correct answer does not depend on: S, wt.
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