For Figure P4.31, the equilibrium position corresponds to x = 0. Neglect the masses of the pulleys and assume that the cable is inextensible, and use conservation of energy to derive the equation of motion in terms of x.

Problem 4.31

For Figure P4.31, the equilibrium position corresponds to x = 0. Neglect the masses of the pulleys and assume that the cable is inextensible, and use conservation of energy to derive the equation of motion in terms of x.

Step by step solution

Step 1 of 3

Due to the arrangement of the pulley,if mass moves by distance ,the mass moves by distance

Thus,the velocity of mass is

The velocity of mass is

The total kinetic energy is

Substituting the values of velocities,we get