Phase Difference of Two Particles in SHM

[JasonV]

Two particles execute simple harmonic motion of the same amplitude and frequency along close parallel lines. They pass each other moving in opposite directions each time their displacement is half their amplitude. What is their phase difference?

 

[Shooting Star]

You haven't shown any attempt. But I'm still giving you a lot of hint. The rest is upto you.

For a particle executing shm, if x=a/2, then a/2=a*sin(wt) => sin(wt) = ½ = sin pi/6 or sin(pi-pi/6). Can you find the phase diff now?

 

[ogb p]

The phase difference between two particles in simple harmonic motion is the difference in their positions at a given point in time. In this scenario, the two particles are moving along parallel lines with the same amplitude and frequency, but in opposite directions. This means that they will pass each other at the midpoint of their motion, when their displacement is half their amplitude.

At this point, the two particles will have the same position, but they will be moving in opposite directions. This results in a phase difference of 180 degrees or π radians. This phase difference will remain constant throughout their motion, as they continue to pass each other at the midpoint of their motion.

It is important to note that the phase difference is dependent on the amplitude and frequency of the motion, and in this specific scenario, the amplitude is half of the wavelength. Therefore, if the amplitude or frequency were to change, the phase difference would also change accordingly.

In conclusion, the phase difference between two particles in simple harmonic motion, moving along close parallel lines with the same amplitude and frequency, and passing each other at the midpoint of their motion, is 180 degrees or π radians.