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Are all mechanical waves simple harmonic waves? Like in all (or most) mechanical waves, do all particles perform Simple Harmonic Motion?

If not then what are the examples? And do different types of waves have different solutions?

Like if it is not a simple harmonic wave/ plane progressive wave then does it have a different equation/solution other than y=sin(wt-kx) What could be the different forms?

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Are all mechanical waves simple harmonic waves ?

No. SHM is just the simplest form of wave or oscillatory motion, which is why it is presented first in mechanics/dynamics courses.

Next step in complexity is to add a damping term to get damped harmonic motion.

Or you can add multiple simple harmonic waves with different periods to get a more complex waveform - for example, the different timbres of sound waves arise because of different combinations of harmonics and different amounts of damping.

There are also quite simple mechanical systems with very complex (and ultimately chaotic) oscillatory motions - an example is the double pendulum.

But everything starts with SHM because you have to learn to walk before you can run.

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  • $\begingroup$ Could you give some examples of mechanical waves where the particles are not performing SHM ? $\endgroup$ Commented Feb 8, 2023 at 18:10
  • $\begingroup$ Nonlinear acoustics, for example. $\endgroup$ Commented Feb 8, 2023 at 18:59
  • $\begingroup$ @TrishaShah I did. Damped harmonic motion is not SHM. Sound waves are not SHM (apart from a simple sine wave). The double pendulum is not SHM. Ocean waves are not SHM. Almost every oscillatory wave in nature is not SHM. $\endgroup$
    – gandalf61
    Commented Feb 8, 2023 at 19:11

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