@ In a spring$-$mass system, the mass is m and the spring constant is k $.$ The critical damping coefficient of the system is $0\mathrm{.}1k\frac{g}{s}.$ In another spring$-$mass system, the mass is $2$ m and the spring constant $8$ k $.$ The critical damping coefficient $($in $k\frac{g}{s})$ of this system is$-$

@ A rigid uniform rod $AB$ of length $L$ and mass $m$ is hinged at $C$ such that $AC=\frac{L}{3},CB=2\frac{L}{3}.$ Ends A and $B$ are supported by springs of spring constant $k.$ The natural frequency of the system is given by

$\sqrt[\phantom{2}]{\frac{K}{m}}$

$\sqrt[\phantom{2}]{\frac{K}{2m}}$

$\sqrt[\phantom{2}]{\frac{2K}{m}}$

$\sqrt[\phantom{2}]{\frac{5K}{m}}$

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