Does Amplitude Affect the Oscillation Period in Harmonic Motion?

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SUMMARY

The oscillation period T of an ideal harmonic oscillator, defined by the equation T = 2π * sqrt(M/k), is independent of the amplitude of motion. In the discussion, a massless spring with a spring constant k = 6 and mass M = 0.04 was analyzed for two different amplitudes: 0.04m and 0.10m. While the theoretical model suggests that the period remains constant regardless of amplitude, real-world systems deviate from this ideal due to factors such as non-ideal spring behavior and large displacements. Consequently, practical oscillation frequencies can vary with amplitude, particularly in systems that do not adhere strictly to Hooke's law.

PREREQUISITES
  • Understanding of harmonic motion principles
  • Familiarity with Hooke's law and spring constants
  • Basic knowledge of oscillation frequency and period calculations
  • Concept of ideal vs. non-ideal systems in physics
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  • Study the effects of non-ideal conditions on harmonic oscillators
  • Explore the mathematical derivation of the oscillation period for different systems
  • Investigate the limitations of Hooke's law in real-world applications
  • Learn about the behavior of pendulums under varying displacement conditions
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Physics students, educators, and engineers interested in the principles of harmonic motion and the practical implications of oscillation theory.

algorith01
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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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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.
 
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.
 

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