Phase Angle for Simple Harmonic Motion

[mneox]

Phase Angle / Phase Question - Simple Harmonic Motion

Homework Statement

If I were given a function of displacement for simple harmonic motion in the form of:

x = Acos($$\omega$$t + $$\phi$$)

Would the phase angle, $$\phi$$, always be the same? Say if I derived the equations into forms for velocity and acceleration as well. The phase angle would not change.. is that correct?

Also, I am confused about what is the phase and what is the phase angle? My textbook lists the "phase angle" as $$\phi$$ and some other sources list "phase" as ($$\omega$$t + $$\phi$$). What's the difference between these??

Homework Equations

x = Acos($$\omega$$t + $$\phi$$)
v = -$$\omega$$Acos($$\omega$$t + $$\phi$$)
a = -$$\omega$$²Acos($$\omega$$t + $$\phi$$)

The Attempt at a Solution

My belief is that it wouldn't change, but I want to be 100% sure.

Thanks for your clarification!

 

[mneox]

Hi, sorry to "bump" a thread but it's been a while now and I still want some clarity on this. Can anyone offer help?

 

[n.karthick]

As far as your first question is concerned, phase does not change if you take derivative of 'x' as long as the phase is independent of time.

 

[ehild]

It is better to call Φ "the phase constant" It is not really angle, as no angle is involved in the SHM. Φ does not change if you calculate the time derivatives of the displacement. The phase is ωt+Φ. It depends on time. When x=Acos(ωt+Φ) has its maximum value the phase is 2kΠ (k is integer). And x=0 if ωt+Φ=(k+1/2)Π . ehild

 

[rwisz]

I can confirm that the phase angle, denoted by \phi, remains constant throughout the simple harmonic motion. This means that no matter what form the equation is expressed in (displacement, velocity, or acceleration), the phase angle will remain the same.

The phase angle represents the initial starting point of the motion and is an important parameter in determining the behavior of the system. It is usually measured in radians and can range from 0 to 2\pi.

The phase, on the other hand, is the combination of the angular frequency (\omega) and the phase angle (\phi). It is expressed as (\omegat + \phi) and represents the current position in the oscillation cycle.

In summary, the phase angle is a fixed value that determines the starting point of the motion, while the phase is a variable that changes as the system oscillates. I hope this clarifies the difference between the two terms.