# Phase angle and Phase in Simple harmonic motion

• Yoseph Santoso
The phase angle is a measure of how far the wave has progressed since the last time it was observed.In summary, the international book uses a different symbol for the phase angle and the Indonesian book uses a different notation for the phase.

#### Yoseph Santoso

I'm a teacher at a Senior High School in Indonesia. I have two Senior High School physics books (Indonesian book) written about simple harmonic motion formula:

y = A sin θ = A sin (ωt + θ0) = A sin 2πφ = A sin 2π (t/T + θ0/2π)
phase angle = θ = ωt + θ0
phase of wave = φ = t/T + θ0/2π​

But I have another book, a university student physics book (International book), written:

y = A sin (ωt + φ)
phase angle = phase of wave = φ​

Are there some things wrong with my Indonesian Senior High School books? Or maybe the writers have a purpose that I haven't known yet? Thanks.

It is just different notation. What the international book calls ##\phi## the Indonesian book is calling ##\theta_0##. There is nothing inherently wrong or right with either choice, although I think the notation used by the international book is more common. At least, it is the notation used in the books I studied.

I mean not for the symbol or notation φ with θ0 , Dale. My Indonesian book differentiate phase angle and phase itself. Phase angle = ωt + θ0 (in degree or radian unit) and phase = t/T + θ0/2π (doesn't have any unit).
Are "phase angle" and "phase" of the wave considered as exactly the same or different?

In that usage phase is in units of cycles and phase angle is in units of radians. It’s a little idiosyncratic, but not wrong.

If you want to use the Indonesian book for some reason I think it is OK. You may just want to prepare your students for the future to know that different textbooks use different conventions. The math is the same, just the labels are different.

• Yoseph Santoso
Okay I see. I think maybe that Indonesian books writers want to make easy the readers to understand the phase "angle" that mostly refer to degree or radian unit. Do you think so?

In relations like ##y = \sin(\omega t+\phi)## the college-level introductory physics textbooks here in the US usually refer to ##\phi## as the phase angle and sometimes ##(\omega t+\phi)## as the phase.

I’ll add my vote. In my experience when someone says “phase” I usually expect them to mean “phase angle” in angular units, not fractions of a wavelength.

On the other hand I will say that in some contexts we will discuss phase errors and then say “A is 1/4 wave ahead of B” or something like that. However we explicitly say “wave” so everyone understands the units, and although we may be discussing phase we don’t often explicitly call the “waves” the “phase” in the same sentence.

No hard rule either way though. All that really matters is that everyone understands your choice.

• Dale
Simple harmonic motion is not the description of a wave. There is no Wavelength involved as nothing progressed. This thread is not discussing its actual title.
The expression for a wave has time and distance terms in it. There can also be a constant term to describe the offset or phase. That constant can either represent a change of time origin or distance origin.

## 1. What is phase angle in simple harmonic motion?

Phase angle in simple harmonic motion is a measurement of the position of an object in its oscillatory cycle. It is typically represented by the Greek letter phi (φ) and is measured in radians.

## 2. How is phase angle related to frequency and period in simple harmonic motion?

The phase angle is directly related to the frequency and period in simple harmonic motion. It is calculated as the product of the frequency and the time, or the ratio of the period and the time.

## 3. Can the phase angle in simple harmonic motion be negative?

Yes, the phase angle in simple harmonic motion can be negative. This occurs when the object is behind its starting position in its oscillatory cycle.

## 4. What is the difference between phase angle and phase in simple harmonic motion?

Phase angle and phase are often used interchangeably, but there is a slight difference between the two. Phase angle refers to the measurement of the position of an object in its oscillatory cycle, while phase is the actual position of the object in the cycle at a given time.

## 5. How is the phase angle in simple harmonic motion affected by changes in amplitude?

The phase angle in simple harmonic motion is not affected by changes in amplitude. This is because the phase angle is solely dependent on the frequency and period of the motion, which remain constant regardless of changes in amplitude.