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equilibrium. There must be a restoring force acting on the oscillating object. The direction of this force must always point toward the equilibrium, and its magnitude must be directly proportional to the magnitude of the object's displacement from its equilibrium position. Mathematically, the restoring force F is given by F = -kx, where x is the displacement from equilibrium and k is a constant that depends on the properties of the oscillating system. The resistive forces in the system must be reasonably small. In this problem, we will introduce some of the basic quantities that describe oscillations and the relationships among them. Part E Which points on the x axis are located a distance A from the equilibrium position? R only Q only both R and Q Part F Suppose that the period is T. Which of the following points on the t axis are separated by the time interval T? K and L K and M K and P L and N M and P Now assume for the remaining Parts G - J, that the x coordinate of point R is 0.12 m and the t coordinate of point K is 0.0050 s. Part G What is the period T ? Express your answer in seconds.

          equilibrium.
There must be a restoring force acting on the oscillating object. The direction of this force must always point toward the equilibrium, and its magnitude must be directly proportional to the magnitude of the object's displacement from its equilibrium position. Mathematically, the restoring force F is given by F = -kx, where x is the displacement from equilibrium and k is a constant that depends on the properties of the oscillating system.
The resistive forces in the system must be reasonably small.
In this problem, we will introduce some of the basic quantities that describe oscillations and the relationships among them.
Part E
Which points on the x axis are located a distance A from the equilibrium position?
R only
Q only
both R and Q
Part F
Suppose that the period is T. Which of the following points on the t axis are separated by the time interval T?
K and L
K and M
K and P
L and N
M and P
Now assume for the remaining Parts G - J, that the x coordinate of point R is 0.12 m and the t coordinate of point K is 0.0050 s.
Part G
What is the period T ?
Express your answer in seconds.

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equilibrium.
There must be a restoring force acting on the oscillating object. The direction of this force must always point toward the equilibrium, and its magnitude must be directly proportional to the magnitude of the object's displacement from its equilibrium position. Mathematically, the restoring force F is given by F = -kx, where x is the displacement from equilibrium and k is a constant that depends on the properties of the oscillating system.
The resistive forces in the system must be reasonably small.
In this problem, we will introduce some of the basic quantities that describe oscillations and the relationships among them.
Part E
Which points on the x axis are located a distance A from the equilibrium position?
R only
Q only
both R and Q
Part F
Suppose that the period is T. Which of the following points on the t axis are separated by the time interval T?
K and L
K and M
K and P
L and N
M and P
Now assume for the remaining Parts G - J, that the x coordinate of point R is 0.12 m and the t coordinate of point K is 0.0050 s.
Part G
What is the period T ?
Express your answer in seconds.

Added by Margaret P.

Calculus: Early Transcendentals

William Briggs, Lyle Cochran, Bernard… 3rd Edition

Chapter 3

Instant Answer

Solved by Expert Kirsty Gledhill

11/29/2023

Step 1

When the block is pulled to the right a distance A, it is at point R. When the block is pushed to the left a distance A, it is at point Q. Show more…

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Consider a block of mass m attached to a spring with force constant k, as shown in the figure (Figure 1). The spring can be either stretched or compressed. The block slides on a frictionless horizontal surface, as shown. When the spring is relaxed, the block is located at x=0. If the block is pulled to the right a distance A and then released, A will be the amplitude of the resulting oscillations. Assume that the mechanical energy of the block-spring system remains unchanged in the subsequent motion of the block.

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Transcript

00:01 Ok, so you've got a block undergoing simple harmonic motion.

00:04 Now all of the questions reference points like k, l, m, n, p, q, r, and i can't see a picture with any of these points labelled on it.

00:17 What i'm guessing is that you've got a graph that looks a bit like this where you've got displacement on the y -axis and time on the x -axis, and you've got that the motion looks something like this.

00:47 And then you're going to have different points labelled on it.

00:51 And so what i'm going to do is i'm going to work on this graph and then tell you how to answer the questions if certain points were called certain things.

01:02 So for example for part e, we're asked which points on the x -axis are located at a distance a from the equilibrium position.

01:10 So the points at a distance a from the equilibrium position are any of the peaks or troughs.

01:22 So they are the points which i'm going to colour in red now.

01:28 So this is a distance a, this is a distance a, it's basically the furthest points from the equilibrium.

01:34 The middle line is the equilibrium position, that's x equals zero.

01:40 And so these are all the peaks and troughs.

01:42 So if r and q are both points among these red ones which i've coloured in, you'll select both of them.

01:51 If only one of them is, then you just pick the one which is at the relevant point.

01:57 Part f asks which points are separated by the period.

02:03 So the period is just the time taken for the waveform to undergo a complete cycle...

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