Question: For the system represented in this Figure, a ) Use Lagrange's formula to find the equations of motion. b ) Determine the natural frequencies of

For the system represented in this Figure,
a) Use Lagrange's formula to find the equations of motion.
b) Determine the natural frequencies of the system and the vibration mode shapes, by taking into considerations the following numerical values:
Mass of the Pulley: m=2kg
Translating Mass: M=10kg
Radius of the Pulley: R=10cm
First Stiffness: k1=40Nm
Second Stiffness: k2=60Nm
For the system represented in this Figure, a )

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