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How to solve this differential equation?

  1. May 25, 2015 #1
    It has been a while since I was involved with my differential equations. I am a mech student. I was trying out a sample problem from the dynamics book and came upon this equation.

    k = some constant of proportionality for a spring pushing back a spring mounted slider.

    (1/k) arcsin(ks/v_0) = t --> becomes s = (v_0/k) sin(kt)

    which is an expression for displacement. I want to know how it is solved for displacement s.

    Thank you.
     
  2. jcsd
  3. May 25, 2015 #2
    If you have an equation like ##arcsint=a## you can write it ##sina=t## here
    (1/k) arcsin(ks/v0)=t
    arcsin(ks/v0)=tk
    then here apply what I did then we get
    sin(tk)=ks/v0
    then simply s is ;
    sin(tk)v0/k=s
     
  4. May 25, 2015 #3
    Thank you. It reminded me of when I solve for theta in some other equations and it rightly should make sense.
     
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