Tooth interference in an external involute spur gear pair can be reduced by

For the epicyclic gear arrangement shown in the figure, $${{\omega _2} = 100}$$ rad/s clockwise (CW) and $${{\omega _{arm}} = 80}$$ rad/s counter clockwise (CCW). The angular velocity $${{\omega _5}}$$ (in rad/s) is

The natural frequency of a spring-mass system on earth is $${\omega _n}.$$ The natural frequency of this system on the moon (g_moon = g_earth/6) is

A mass $$m$$ attached to a spring is subjected to a harmonic force as shown in the figure. The amplitude of the forced motion is observed to be $$50$$ mm. The value of m (in kg) is