Energy changes in mass spring system

Thread starter Asad Raza
Start date Dec 8, 2016
Tags

Energy Mass Mass spring system Simple harmonic motion Spring System

AI Thread Summary

The discussion focuses on the relationship between kinetic energy and velocity in a mass-spring system, specifically questioning why the kinetic energy versus time curve mirrors the modulus of the velocity time curve. It outlines a mathematical approach to prove this by considering the general trajectory of a harmonic oscillator, expressed as x(t)=Acos(ωt)+Bsin(ωt). The next step involves differentiating this equation to derive the velocity function v(t). Finally, the kinetic energy K(t) is calculated using the formula K(t)=1/2 mv(t)^2. This analysis aims to clarify the connection between kinetic energy and velocity in harmonic motion.

Dec 8, 2016

Asad Raza

Why is the kinetic energy vs time curve of a mass spring system is just a modulus of respective velocity time curve.
How can we prove it mathematically ?

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Dec 8, 2016

ShayanJ

Science Advisor

Insights Author

Actually that's not true!
Step1) Consider the most general trajectory for a harmonic oscillator:## x(t)=A\cos \omega t+B\sin\omega t ##
Step2) Differentiate it w.r.t. time to get the velocity ##v(t)##.
Step3) Put ##v(t)## in ##K(t)=\frac 1 2 m v(t)^2 ##.

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