Why Do mω²xa and 2kxa Both Act in Normal Modes Oscillations?

[LCSphysicist]

Homework Statement

All below

Relevant Equations

All below

I am not sure if i get this part of a book i am using:

Why are the mwo²xa acting too? Is not 2kxa enough?

 

[LCSphysicist]

Ignore it, i made a confusion :P need to sleep.

 

[ehild]

Homework Statement:: All below
Relevant Equations:: All below

View attachment 266042

I am not sure if i get this part of a book i am using:

View attachment 266043

Why are the mwo²xa acting too? Is not 2kxa enough?

It is due to gravity.