Q$.3$ A spring$-$mass system is subjected to a harmonic force of variable frequency. The amplitude at $2$ Hz is found to be $4$ mm in phase and $1\mathrm{.}2$ mm out of phase at $12$ Hz $.$ For the mass $m=2kg,$ find the stiffness of the spring $k$ and the amplitude of the harmonic force $F_0.$

Ans. $k=2867\frac{N}{m},F_O=10\mathrm{.}2N$