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