(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

We have the differential equation x''=a*x. If a=0 then the motion is:

X(t)=Xo+Vo*t [1]

a)Prove (by solving the dif. equation) for a<>0 (both a>0 and a<0) that when we take the limit a->0, motion will be given by [1].

b)BUT "a" has units [T^-2] and 0 is just a number, so the limit a->0 is not well defined. What is the correct form of the limit?

2. Relevant equations

3. The attempt at a solution

I have some problem with question b.

If 0 is just a number then we must have a simple number on the left side of the limit. So i assume that i have to write it this way:

a[T^2]-->0

so that the units of "a" (T^-2) and T^2 will cansel its other.

What do you think?

PS. Sorry for my bad english.. I translated it from greek to english

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# Homework Help: Solving differential equation x'' = ax

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