Two plates of the same metal having equal thickness are to be butt welded with electric arc. When the plate thickness changes, welding is achieved by

The sun gear in the figure is driven clockwise at 100 rpm. The ring gear is held stationary. For the number of teeth shown on the gears, the arm rotations at

A spring mass $$-$$ dashpot system is shown in the figure. The spring stiffness is $$K,$$ mas is $$m$$, and the viscous damping coefficient is $$c$$. The system is subjected to a force $$\,{F_0}\cos \omega t\,\,$$ as shown. Write the equations of motion which are needed to determine $$x.$$ (No need to determined $$x.$$)

The assembly shown in the figure is composed of two massless rods of length $$l$$ with two particles, each of mass $$m$$. The natural frequency of this assembly for small oscillations is