What does phase of the motion in terms of cosine displacement mean?

In summary, the question is asking what the phase of the motion, represented by the function x(t) = A*cos(wt-phi), is in terms of cosine displacement. This means finding the displacement of the function from the predefined 0 point. The answer can be found by calculating the value of phi in the function.
  • #1
Maskawisewin
3
0
What does "phase of the motion in terms of cosine displacement" mean?

I'm getting tripped up on the wording of this homework question.

Homework Statement


Measured acceleration: An accelerometer has measured the simple harmonic motion shown in the image below.

Homework Equations


You want to describe the position as a function of time as a cosine: [itex]x(t)=A\cos(\omega t-\phi)[/itex].
What is the phase of the motion shown in the graph (in terms of a cosine displacement)?
droHh.jpg


The Attempt at a Solution


I've tried reading my textbook for "phase of the motion". There's a section that talks about a rotating vector phasor that references the unit circle. Is this the right path? Are they talking about what the cosine is calculating (i.e. what's inside the brackets of the cosine)?
 
Last edited:
Physics news on Phys.org
  • #2


The phase of a periodic function is the displacement the function has from some predefined 0 point. For example, sin(x) is 90° out of phase from cos(x). The question is just asking for [itex]\phi[/itex] in [itex]x(t) = A\cos(\omega t+\phi)[/itex].
 
  • #3


Thank you.
 

1. What is the meaning of "phase of the motion" in terms of cosine displacement?

The phase of the motion refers to the position of an object at a specific point in its oscillation or vibration cycle. In terms of cosine displacement, it is a measure of how far the object has moved from its equilibrium position at a given time.

2. How is the phase of motion related to the amplitude of the cosine displacement?

The phase of motion and the amplitude of the cosine displacement are not directly related. The amplitude represents the maximum displacement from the equilibrium position, while the phase refers to the specific position of the object at a given time in its cycle.

3. Can the phase of motion change during an object's oscillation?

Yes, the phase of motion can change during an object's oscillation. This can happen if there is a change in the amplitude, frequency, or initial conditions of the motion. It can also change if external forces are applied to the object.

4. How is the phase of motion measured?

The phase of motion is typically measured in degrees or radians. It can be calculated by comparing the position of the object at a certain time to its equilibrium position, and then converting that difference into degrees or radians.

5. Does the phase of motion affect the period of an object's oscillation?

No, the phase of motion does not affect the period of an object's oscillation. The period is determined by the frequency of the motion and the properties of the object, such as its mass and stiffness. The phase only indicates the position of the object at a specific point in its oscillation cycle.

Similar threads

  • Introductory Physics Homework Help
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
11
Views
3K
  • Introductory Physics Homework Help
Replies
4
Views
19K
  • Introductory Physics Homework Help
Replies
8
Views
5K
  • Introductory Physics Homework Help
Replies
15
Views
4K
  • Introductory Physics Homework Help
Replies
9
Views
3K
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
24
Views
2K
Back
Top