Method Based on D'Alembert's Principle:
In dynamic condition the free body diagram of mass might be drawn as follows :
Figure 3
The free body diagram of mass is illustrated in above Figure 3. The force equation may be written as follows:
mx'+ mg = k ( x + Δ) . . . (4)
Incorporating equation. (1) in Eq. (4), the below relation is attained.
mx' + kx = 0
This equation is similar as we attained earlier.