Simple Harmonic Motion: Limitations of T

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SUMMARY

The formula for the period of simple harmonic motion (SHM), T = 2π √(m/k), has limitations primarily when applied to pendulums. While it approximates the motion well under the assumption that the angle θ is small (where sinθ ≈ θ), deviations occur as θ increases. The error in this approximation is proportional to θ²/6, indicating that the formula is most accurate for small angles. Understanding these limitations is crucial for precise applications in physics and engineering.

PREREQUISITES
  • Understanding of simple harmonic motion (SHM)
  • Familiarity with pendulum dynamics
  • Basic knowledge of trigonometric functions
  • Ability to interpret mathematical proofs
NEXT STEPS
  • Study the derivation of the SHM period formula T = 2π √(m/k)
  • Explore the effects of angular displacement on pendulum motion
  • Learn about the limitations of SHM in real-world applications
  • Investigate higher-order corrections to the SHM period for larger angles
USEFUL FOR

Physics students, educators, and engineers interested in the principles of simple harmonic motion and its practical limitations in pendulum systems.

Hardik Batra
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what is the limitation of T = 2π [itex]\sqrt{\frac{m}{k}}[/itex]
 
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Hello Hardik! :smile:

Are you talking about a pendulum?

A pendulum is never exactly shm, but it is very nearly so if we assume θ = sinθ.

Since sinθ = θ - θ3/6 + …

that means the error will be a function of θ2/6 …

to find out what function, just plough through the proof. :wink:




Hardik Batra said:
what is the limitation of T = 2π [itex]\sqrt{\frac{m}{k}}[/itex]
 

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