Please help solve the attachment.
Only like-dimensioned quantities may be added, subtracted, compared, or equated.
As we have addition on the left, the dimensions of each on the left must be the same.
Thus the dimensions of m d^2(x)/dt^2 must be the same as that of c dx/dt and kx
Dimensional Homogeneity requires ...
The solution shows all mathematical steps and gives explanation for each step in a very clear manner.