Solving Simple Harmonic Motion: Oscillatory & Sinusoidal in Time

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SUMMARY

Oscillatory motions in simple harmonic motion (SHM) are fundamentally sinusoidal in time, meaning that the equations governing SHM involve sine and cosine functions. When plotting position as a function of time for SHM, the resulting graph is a sinusoidal wave. This relationship is critical for understanding the periodic nature of oscillations in physics and mathematics.

PREREQUISITES
  • Understanding of simple harmonic motion (SHM)
  • Familiarity with sine and cosine functions
  • Basic knowledge of graphing functions
  • Concept of periodicity in oscillatory systems
NEXT STEPS
  • Study the mathematical derivation of simple harmonic motion equations
  • Explore the properties of sine and cosine functions in oscillatory systems
  • Learn about the graphical representation of SHM
  • Investigate applications of SHM in real-world scenarios
USEFUL FOR

Students of physics and mathematics, educators teaching oscillatory motion, and anyone interested in the mathematical foundations of wave phenomena.

iurod
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Hi,
I having trouble grasping what: "oscillatory motions are sinusoidal in time" means... does this just mean that when solving a problem for simple harmonic motion that the equation is going to involve both and sin/cos and time? Sorry this might be more of a mathematical question.
 
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If you plot the position as a function of time, you'll get a sinusoidal graph. (Yes, descriptions of SHM will involve sines and cosines.)
 

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