Position vs time graph simple harmonic motion phase constant

• Ly444999
In summary, the phase constant cannot be determined solely based on the given information. The function increases at t=0, so the phase constant cannot be π/3. However, there are multiple possible solutions for the phase constant, such as -2π/3, that would give the correct value at t=0. More information is needed to determine the correct phase constant.
Ly444999

Homework Statement

http://imgur.com/a/FDfAp

What is the phase constant?

Homework Equations

x(t) = A*cos(ωt+Φ)

The Attempt at a Solution

If I'm not mistaken at t = 0 the graph starts at half the amplitude or 5. Also the amplitude of this graph is 10, and at t = 0 angular velocity is also 0.
5 = 10*cos(0 + Φ)
Φ = arccos(5/10)
Φ = π/3
The answer is supposed to be -2π/3, I'm not sure what I did wrong or if I'm even doing the question right.

Last edited by a moderator:
Ly444999 said:

Homework Statement

http://imgur.com/a/FDfAp
What is the phase constant?

Homework Equations

x(t) = A*cos(ωt+Φ)

The Attempt at a Solution

If I'm not mistaken at t = 0 the graph starts at half the amplitude or 5. Also the amplitude of this graph is 10, and at t = 0 angular velocity is also 0.
5 = 10*cos(0 + Φ)
Φ = arccos(5/10)
Φ = π/3
The answer is supposed to be -2π/3, I'm not sure what I did wrong or if I'm even doing the question right.
The phase constant is different if you suppose x(t) as x(t) = A*cos(ωt+Φ) or x(t) = A*cos(ωt-Φ) or x(t) = A*sin(ωt+Φ), x(t) = A*sin(ωt-Φ).
You also have to take into account if the function increases or decreases at t=0. The function in question increases, so the phase can not be pi/3. But it does not mean that -2pi/3 is correct.

Ly444999 said:
5 = 10*cos(0 + Φ)
Φ = arccos(5/10)
The arccos function is defined to return a value in a certain range, but there are infinitely many solutions to cos(Φ)=0.5.
What other solutions are there in, say, (-π, π), or (0, 2π) if you prefer?
These all give the right value at t=0, but what about an instant later?

1. What is a position vs time graph in simple harmonic motion?

In simple harmonic motion, a position vs time graph is a graphical representation of the displacement of an object from its equilibrium position over time. It shows how the position of the object changes as time passes.

2. How is the phase constant related to a position vs time graph in simple harmonic motion?

The phase constant, denoted as φ, represents the starting point or initial phase of the motion. It is related to the position vs time graph by determining the position of the object at time t=0. This can be seen as the vertical shift of the graph, with a higher phase constant resulting in a higher starting position on the graph.

3. What does the slope of a position vs time graph represent in simple harmonic motion?

The slope of a position vs time graph in simple harmonic motion represents the velocity of the object. A steeper slope indicates a higher velocity, while a flatter slope indicates a lower velocity. The slope is constantly changing as the object oscillates back and forth.

4. How can we determine the amplitude and period of a simple harmonic motion from a position vs time graph?

The amplitude of the motion can be determined by measuring the distance from the equilibrium position to the highest or lowest point on the graph. The period, which is the time it takes for one complete oscillation, can be determined by measuring the time between two consecutive peaks or two consecutive troughs on the graph.

5. Can a position vs time graph for simple harmonic motion have a negative slope?

Yes, a position vs time graph for simple harmonic motion can have a negative slope. This indicates that the object is moving in the opposite direction of the positive direction on the graph. However, the amplitude and period of the motion will remain the same regardless of the direction of the slope.

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