Simple Harmonic Motion/Wave Motion

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SUMMARY

The discussion focuses on the analysis of the function s = 2sin(2t)cos(2t) to determine the frequency, amplitude, and period of simple harmonic motion. The participant correctly simplifies the function to s = sin(4t), identifying the amplitude (A) as 1, the period (P) as π/2, and the frequency (F) as 2/π. The calculations are confirmed to be accurate, assuming that the variable t is measured in radians.

PREREQUISITES
  • Understanding of trigonometric identities, specifically the product-to-sum formulas.
  • Knowledge of simple harmonic motion concepts, including amplitude, period, and frequency.
  • Familiarity with the sine function and its properties in the context of wave motion.
  • Basic understanding of radians as a unit of angular measurement.
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  • Study the derivation and application of the product-to-sum identities in trigonometry.
  • Explore the relationship between frequency, period, and amplitude in simple harmonic motion.
  • Learn about the graphical representation of simple harmonic motion and wave functions.
  • Investigate the implications of phase shifts in wave motion and their effects on amplitude and frequency.
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Students of physics, educators teaching wave motion concepts, and anyone interested in the mathematical analysis of simple harmonic motion.

pippermay
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Hi,

I need to find the frequency, amplitude, and period for the motion of a particle whose distance s from the origin is the given function.

s= 2sin2tcos2t.

This is what I came up with, can someone please tell me if I am doing this correctly.

sin2t = 2sintcost

s = sin4t

A= 1
P= Pi/2
F= 2/Pi

Thanks.
 
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Looks good to me. (Assuming that 2t is in radians.)
 
Thank you so much
 

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