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B Energy changes in mass spring system

  1. Dec 8, 2016 #1
    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 ?
     
  2. jcsd
  3. Dec 8, 2016 #2

    ShayanJ

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    Gold Member

    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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