Simple Harmonic Motion: Limitations of T

Thread starter Hardik Batra
Start date Mar 20, 2013
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Harmonic Harmonic motion Motion Simple harmonic motion

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The formula T = 2π √(m/k) for simple harmonic motion (SHM) has limitations primarily when applied to systems like pendulums. It assumes small angles, where sin(θ) approximates θ, but this approximation introduces errors as the angle increases. The error in the period T becomes significant when θ is not small, as it is proportional to θ². Therefore, the formula is most accurate for small displacements and fails for larger angles. Understanding these limitations is crucial for accurate applications of SHM principles.

Mar 20, 2013

Hardik Batra

what is the limitation of T = 2π \sqrt{\frac{m}{k}}

Last edited: Mar 20, 2013

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Mar 20, 2013

tiny-tim

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Hello Hardik!

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.

Hardik Batra said:

what is the limitation of T = 2π \sqrt{\frac{m}{k}}

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