Solve SHM Eqn Problem: Max Energy Transformation

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SUMMARY

The discussion focuses on solving a simple harmonic motion (SHM) problem involving a mass on a spring with a spring constant of 3.76 N/m and a position function described by x = (4.55 cm) cos(3.70t rad/s). Participants aim to determine when the potential energy (PE) is changing most rapidly into kinetic energy (KE) within the interval 0 PREREQUISITES

  • Understanding of simple harmonic motion (SHM)
  • Knowledge of potential energy (PE) and kinetic energy (KE) equations
  • Ability to differentiate functions and find critical points
  • Familiarity with trigonometric identities and their applications in calculus
NEXT STEPS
  • Learn how to derive kinetic energy (KE) as a function of time in SHM
  • Study the application of derivatives to find maxima and minima in functions
  • Explore the conservation of energy principles in oscillatory systems
  • Investigate the use of trigonometric identities in simplifying derivatives
USEFUL FOR

Students and educators in physics, particularly those focusing on mechanics and oscillatory motion, as well as anyone interested in understanding energy transformations in simple harmonic systems.

  • #61
Recheck your arithmetic.
 
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  • #62
I have twice and i still get the same answer...where are you looking... or can you point it out because this questions has been driving me up the wall for almost two days. So if possible can you point out exactly where i went wrong because obviously you know that i know what i am doing.
 
  • #63
I suspect you are dropping an \omega.
 
  • #64
I don't believe i am...i am using the exact d(KE)/dt equation that i posted a few posts ago. So as far as i know i am not. What numeric value do you get.? If you choose to calculate it i will redo the question showing you exactly what i am doing.
 
  • #65
1.06

cos(3.70)(1.06)=-0.710627
sin(3.70)(1.06)=-0.703568948

coswtsinwt=0.499975091

so now that i manipulate the d(KE)/dt i get:

KA^2wcoswtsinwt
A=0.0455 m
K=3.76 N/m

(3.76)(2.07025e-3)(3.70)(-0.710627)(-0.703568948)
=0.0143999 J/s
 
  • #66
You are a good man DOC AI...a very good man

thank you so much for your help...i probably drove you up the wall with this question but you stood by me

truly a super mentor

:biggrin:
 

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