# Quick Question on Harmonic Motion

## Main Question or Discussion Point

Is the oscillation period T ( T = 2╥ * sqrt(M/k) ) independent of the Amplitude of the motion? I mean the equation shows that it is but I'm not totally convinced.

For example, if a massless spring of k = 6 and M = 0.04 has the mass pulled down (i) 0.04m and then (ii) 0.10m. Will the oscillation period T be the same for both amplitudes (i and ii)?

Thanks in advance for any help.

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phyzguy
For an ideal harmonic oscillator, yes, the frequency is independent of the amplitude. Of course, no real system is ideal - i.e. massless springs do not exist. So in practice any real system has a frequency that depends on the amplitude.

Nabeshin
Indeed! This is one of the big to-do's about harmonic oscillators! The frequency of oscillation (or equally, the period) does not depend on the initial conditions! Phyzguy points out one regime where a system fails to be a harmonic oscillator. Others include a pendulum where the displacement is not small, or a spring which is stretched so much that hooke's force law is no longer accurate.