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woodie37

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**Help solving 2nd order differential equation plz**

While solving for the time it takes an object of mass, m, with initial velocity, v, to compress a spring with spring constant, k to the maximum compression, I came accross the following differential equation

m(d[tex]^{2}[/tex]x/dt[tex]^{2}[/tex]) = kx - mg

I drew a f.b.d. of the forces on the object, mg down and kx (force of spring) up, and that's why I got kx - mg as the net force, the spring is on the bottom.

Can someone show me the technique to solving this please? I'm in grade 12 and have never learned differential equations before, but I finished both integration and differentiation calculus on my own in the summer.