Derivation of an S.H.M. Equation

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SUMMARY

The discussion focuses on deriving the equation for Simple Harmonic Motion (S.H.M.), specifically T = 2π√(m/k). Participants emphasize the importance of understanding the relationship between acceleration and displacement in oscillators. By applying Newton's second law (F = ma), the acceleration can be expressed in terms of displacement, leading to the conclusion that a = -ω²x, where ω is the angular frequency. This relationship ultimately allows for the derivation of the period T in terms of mass m and spring constant k.

PREREQUISITES
  • Understanding of Newton's second law (F = ma)
  • Familiarity with concepts of angular frequency (ω)
  • Knowledge of displacement in oscillatory motion
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the derivation of the equation a = -ω²x in detail
  • Learn about the physical significance of angular frequency (ω)
  • Explore the relationship between mass (m) and spring constant (k) in oscillatory systems
  • Investigate different models of harmonic motion beyond S.H.M.
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Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to explain the derivation of S.H.M. equations.

fatboy_1989
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Can anybody show me how to derive the equation for SHM. (T = 2 x (Pie) x (root m/k))

Help would be greatly appreciated, as i need it for coursework
 
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No one will show you, but we will help you along it deriving it yourself.
How can you model harmonic motion? What function would you use?
 
it depends on cases. but I can give you the general way

first you should find the relationship between the acceleration of oscillator and its displacement

Then, by means of Newton's second law, F=ma
find the a in terms of x if a is directly proportional to minus x
then, for S.H.M a = -w^2x , where w is the angular frequency of motion
w = =2pi/T
T=2pi/w
 

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