# How to solve this differential equation?

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1. May 25, 2015

### LeDragonian

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. May 25, 2015

### Quarlep

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

3. May 25, 2015

### LeDragonian

Thank you. It reminded me of when I solve for theta in some other equations and it rightly should make sense.