In a mechanical system, the static deflection value was measured as 2.48 mm. In a free vibration test for this mechanical system, the free vibration curve measured with an initial displacement of 0.1 m is given in the graph on the side. The amplitude values for different moments in the free vibration response are shown in the figure. Write the equation of motion for the free vibrations of the system. The amplitude-time graph of the mechanical system is as follows. 

Genlik (m) 0.12 0.1 0.08 0.06 0.04 0.02 -0.02 -0.04 -0.06 -0.08 -0.10 0.06032 m 0.2 0.4 0.008025 m im 0.6 Zaman (sn) 0.8