a A pendulum consists from a massless rod with spherical bod

a) A pendulum consists from a massless rod with spherical bodies on both ends. Length of the rod is l. Masses are given on the picture. The distance from the axis of rotation to the lighter sphere is l/3. A static frame supports the pendulum. Calculate the angular frequency of small oscillations of the pendulum. Neglect friction.

b) Now consider the frame that holds the pendulum in a) is placed on the block with mass 6m. Calculate the angular frequency of pendulum oscillations again. There is no friction in the system.

Solution

We can use the torque equation to solve this problem as the unknown force due to the rod will pass through the hinge.

Hence we can write the torque equation as

2mg * 2/3 L * sin(theta) - mg *L/3 *sin (theta) = 2m (4/9 L²) + m (L²/9) * alpha

g (theta) = L alpha (smalll angle approximation)

Hence angular frequency , sqrt (g/L)

Please post seperate question as seperate