Explanation of formula T = 2pi sqrt(m/k)

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SUMMARY

The formula T = 2π√(m/k) represents the period of a simple harmonic oscillator, derived from Hooke's law (F = -kx) and the principles of energy conservation. The total energy in the system is expressed as E(total) = 0.5mv² + 0.5kx², linking mass (m) and spring constant (k) to the oscillation period. Understanding the derivation involves analyzing acceleration graphs of simple harmonic motion (SHM) to connect these concepts effectively.

PREREQUISITES
  • Understanding of Hooke's Law (F = -kx)
  • Familiarity with energy conservation principles in mechanics
  • Basic knowledge of simple harmonic motion (SHM)
  • Ability to interpret graphs related to acceleration in SHM
NEXT STEPS
  • Derive the equation for acceleration in simple harmonic motion from SHM graphs
  • Study the relationship between mass, spring constant, and oscillation period
  • Explore energy conservation in oscillatory systems
  • Investigate real-world applications of simple harmonic motion in engineering
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to clarify the derivation of oscillation formulas.

jackrc11
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Homework Statement


This formula we've been using recently, I don't understand where it comes from.

Homework Equations


T = 2pi * sqrt(m/k)

The Attempt at a Solution


Hooke's law: F = -kx
E(total) = .5mv^2 + .5kx^2
Circumference of a Circle: C = 2 * pi * r

I figure these piece together, but I don't understand how.
 
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jackrc11 said:

Homework Statement


This formula we've been using recently, I don't understand where it comes from.

Homework Equations


T = 2pi * sqrt(m/k)

The Attempt at a Solution


Hooke's law: F = -kx
E(total) = .5mv^2 + .5kx^2
Circumference of a Circle: C = 2 * pi * r

I figure these piece together, but I don't understand how.

You have to derive the equation for acceleration from a graphs of Shm. Look at them and try to get an equation for acceleration.

a = - w2A
Now you can get that equation easily
Previous thread: https://www.physicsforums.com/threads/deriving-angular-frequency-for-simple-harmonic-motion.219104/
 
Last edited:

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