In a certain slider-crank mechanism, lengths of crank and connecting rod are equal. If the crank rotates with a uniform angular speed of 14 rad/s and the crank length is 300 mm, the maximum acceleration of the slider (in m/s²) is _________

The number of degrees of freedom of the planetary gear train shown in the figure is

In a spring-mass system the mass is m and the spring constant is $$k$$. The critical damping coefficient of the system is $$0.1$$ kg/s. In another spring mass system, the mass is $$2m$$ and the spring constant is $$8k$$. The critical damping coefficient (in kg/s) of this system is __________

A single-degree-freedom spring mass system is subjected to a sinusoidal force of $$10$$ N amplitude and frequency $$\omega $$ along the axis of the spring. The stiffness of the spring is $$150$$N/m, damping factor is $$0.2$$ and the undamped natural frequency is $$10$$$$\omega $$. At steady state, the amplitude of vibration (in m) is approximately