A force $$P$$ is applied at a distance $$x$$ from the end of the beam as shown in the figure. What would be the value of $$x$$ so that the displacement at $$'A'$$ is equal to zero?

Two solid circular shafts of $${{R_1}}$$ and $${{R_2}}$$ are subjected to same torque. The maximum shear stresses developed in the two shafts are $${\tau _1}$$ and $${\tau _2}.$$ If $${{{R_1}} \over {{R_2}}} = 2,$$ then $${{{\tau _1}} \over {{\tau _2}}}$$ is _______.

Consider a single degree-of-freedom system with viscous damping excited by a harmonic force. At resonance, the phase angle (in degree) of the displacement with respect to the exciting force is

A mass-spring-dashpot system with mass m = 10 kg, spring constant k = 6250 N/m is excited by a harmonic excitation of 10 cos(25t) N. At the steady state, the vibration amplitude of the mass is 40mm. The damping coefficient (c, in N.s/m) of the dashpot is ______________