.......................................................................... (2.5.28)

Similarly velocity of mass M is ....................................................(2.5.29)

Hence, kinetic energy of the system which is due to the kinetic energy of the mass M and the kinetic energy of link with mass m is

........................................................................ (2.5.30)

.........................................................(2.5.31)

The potential energy of the system is due to the spring element and also due to the change in height of the link. Considering a hard spring with cubic nonlinearity, the potential energy V of the system can be given by the following equation.

....................................................................... (2.5.32)

As two forces are acting on the system, to find the generalized force first we have to find the position vector of the point where the forces are acting. For the force the position vector from the fixed coordinate system is . Similarly, for the second force which is acting on the pivoted link is . So the generalized forces can be obtained by using Eq. (2.5.18) as follows.

......................................................................................................... (2.5.33)

...(2.5.34)

...(2.5.35)

Now using Lagrange Principle

............................................................................................... (2.5.36)