Item 1Learning Goal:To understand the application of the general harmonic equation to the kinematics of aspring oscillator.One end of a spring with spring constant k is attached to the wall. The other end isattached to a block of mass m. The block rests on a frictionless horizontal surface. Theequilibrium position of the left side of the block is defined to be x = 0. The length of therelaxed spring is L. (Figure 1)The block is slowly pulled from its equilibrium position to some position init> 0 along thex axis. At time t = 0, the block is released with zero initial velocity.The goal is to determine the position of the block (t) as a function of time in terms of wand initIt is known that a general solution for the displacement from equilibrium of a harmonicoscillator isx(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 initFigure1 of 3LXinitwinx = 0Part AUsing the general equation for x (t) given in the problem introduction, express the initial position of the block init in terms of C, S, and w (Greek letter omega).► View Available Hint(s)IVE ΑΣΦ?Tinit =SubmitPart B Complete previous part(s)Part C Complete previous part(s)Now, imagine that we have exactly the same physical situation but that the x axis is translated, so that the position of the wall is now defined to be x = 0. (Figure 3)The initial position of the block is the same as before, but in the new coordinate system, the block's starting position is given by new (t = 0) = L + init-Part DFind the equation for the block's position new (t) in the new coordinate system.Express your answer in terms of L, Zinit, w (Greek letter omega), and t.► View Available Hint(s)LIVE ΑΣΦ?Tnew (t) =Submit

In the given question, Spring constant = k Length of the relaxed spring = L At t = 0, the block is…

Answered: Using the general equation for z (t)…

Using the general equation for z (t) given in the problem introduction, express the initial position of the block it in terms of C, S, and w (Greek letter omega).

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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Question

Item 1
Learning Goal:
To understand the application of the general harmonic equation to the kinematics of a
spring oscillator.
One end of a spring with spring constant k is attached to the wall. The other end is
attached to a block of mass m. The block rests on a frictionless horizontal surface. The
equilibrium position of the left side of the block is defined to be x = 0. The length of the
relaxed spring is L. (Figure 1)
The block is slowly pulled from its equilibrium position to some position init> 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 (t) as a function of time in terms of w
and init
It is known that a general solution for the displacement from equilibrium of a harmonic
oscillator is
x(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 init
Figure
1 of 3
L
Xinit
win
x = 0
Part A
Using the general equation for x (t) given in the problem introduction, express the initial position of the block init in terms of C, S, and w (Greek letter omega).
► View Available Hint(s)
IVE ΑΣΦ
?
Tinit =
Submit
Part B Complete previous part(s)
Part C Complete previous part(s)
Now, imagine that we have exactly the same physical situation but that the x axis is translated, so that the position of the wall is now defined to be x = 0. (Figure 3)
The initial position of the block is the same as before, but in the new coordinate system, the block's starting position is given by new (t = 0) = L + init-
Part D
Find the equation for the block's position new (t) in the new coordinate system.
Express your answer in terms of L, Zinit, w (Greek letter omega), and t.
► View Available Hint(s)
LIVE ΑΣΦ
?
Tnew (t) =
Submit

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