A mass travels in a straight line on a horizontal plane. It is attached at one end to a fixed vertical wall through a spring (spring constant ) while at the other end, it is connected through an inextensible cable to a pendulum of mass m. The lower mass m will oscillate in the vertical plane ABC and there is no friction. Using the position x of the mass and the angle theta of the mass m, as the configuration variables, write the two equations of motion.

The equations are as below:

Explanation:

As the complete question is not given, the complete question is attached herewith.

From the given data

The mass of the block is M

The length of the spring at any given time is l

The length of the spring initially is lo

The length of the platform is lr

So the coordinates in y and z direction are given as

Now the Lagrange is given as

Now The value is given as

So the 1st equation becomes

Now the second equation is as

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