In the mechanism given below, if the angular velocity of the eccentric circular disc is $$1$$ rad/s, the angular velocity (rad/s) of the follower link for the instant shown in the figure is

Note : $$All$$ $$dimensions$$ $$are$$ $$in$$ $$mm$$

The following are the data for two crossed helical gears used for speed reduction:
Gear $$I:$$ Pitch circle diameter in the plane of rotation 80mm and helix angle 30^o

Gear $$II:$$ Pitch circle diameter in the plane of rotation 120mm and helix angle 22.5^o

If the input speed is 1440 rpm. The output speed in rpm is

A solid disc of radius $$r$$ rolls without slipping on a horizontal floor with angular velocity $$\omega $$ and angular acceleration $$\alpha $$. The magnitude of the acceleration of the point of contact on the disc is

A concentrated mass $$m$$ is attached at the centre of a rod of length $$2L$$ as shown in the figure. The rod is kept in a horizontal equilibrium position by a spring of stiffness $$k.$$ For very small amplitude of vibration, neglecting the weights of the rod and spring, the un damped natural frequency of the system is