Simple Harmonic Motion Phase angle

[Jimmy84]

Homework Statement

What is the initial phase angle of this graph that describes a simple harmonic motion?

Homework Equations

The Attempt at a Solution

I don't have any clue about how to find it by watching the graph, I know only an equation to find it. Any help please.

 

[PeterO]

Homework Statement

What is the phase angle of this graph that describes a simple harmonic motion?

Homework Equations

The Attempt at a Solution

I don't have any clue about how to find it by watching the graph, I know only an equation to find it. Any help please.

I did a quick google search for "phase angle of shm" and the first site offered gave a good lead ... equation 510.
Any of the other offereings may have been just as useful.
Many were to other questions about phase angle here on Physics Forums in fact.

 

[Jimmy84]

I did a quick google search for "phase angle of shm" and the first site offered gave a good lead ... equation 510.
Any of the other offereings may have been just as useful.
Many were to other questions about phase angle here on Physics Forums in fact.

Do you mean this http://farside.ph.utexas.edu/teaching/301/lectures/node138.html ? I already read them but i just started reading the theory about Simple Harmonic Motion yesterday and I am a bit lost with it so is there any way to find the angle just by inspection of the graph? I didnt understand much of the previous posts about the subject on the forum

 

[PeterO]

Do you mean this http://farside.ph.utexas.edu/teaching/301/lectures/node138.html ? I already read them but i just started reading the theory about Simple Harmonic Motion yesterday and I am a bit lost with it so is there any way to find the angle just by inspection of the graph? I didnt understand much of the previous posts about the subject on the forum

That's the one.

I was particularly taken by the sentence before equation :

"Finally, the phase angle phi determines the times at which the oscillation attains its maximum amplitude, x=a: in fact"

If the phase angle was zero, then maximum amplitude would be happening then - so the graph of displacement vs time must look like a Cosine gragh.

A phase angle will translate the graph. Your graph is certainly translated. can you see by how much?

 

[rwisz]

I would recommend using the equation for simple harmonic motion, which is x(t) = A*cos(ωt + φ), where A is the amplitude, ω is the angular frequency, and φ is the phase angle. In this equation, the phase angle represents the initial position of the object at t = 0.

To find the initial phase angle, you can use the given graph to determine the amplitude and angular frequency. Once you have those values, you can plug them into the equation and solve for φ. Alternatively, you can also use the initial and final positions of the object to calculate the phase angle.

It is also important to note that the phase angle can vary depending on the starting point of the oscillation. If the object starts at its equilibrium position, the phase angle would be 0. However, if the object starts at its maximum displacement, the phase angle would be 90 degrees or π/2 radians.

In summary, to determine the initial phase angle of a simple harmonic motion graph, you can use the equation for SHM or use the initial and final positions of the object to calculate it.