• # question_answer For a system of two springs and block system, choose the correct option. A)  for the equilibrium position (about which oscillation occur), the stretch is$x=\frac{mg}{k}$ B)  the time period of oscillation is$2\pi \sqrt{\frac{m}{2k}}$ C)  Both [a] and [b] are correct                                                                D)  Both [c] and [b] are incorrect

Idea When spring of spring constants${{k}_{1}},{{k}_{2}},{{k}_{3}}...$are connected in parallel then their   equivalent   spring constant is given by ${{k}_{eq}}={{k}_{1}}+{{k}_{2}}+{{k}_{3}}...$ 2kx = mg $\Rightarrow$$x=\frac{mg}{2k}$ As springs are in parallel. $\therefore$${{k}_{eq}}=k+k=2k$ So, $T=2\pi \sqrt{\frac{m}{{{k}_{eq}}}}$ $T=2\pi \sqrt{\frac{m}{2k}}$ TEST Edge Question related to series combination of springs can also be asked in that case $\frac{1}{{{k}_{eq}}}=\frac{1}{{{k}_{1}}}+\frac{1}{{{k}_{2}}}+\frac{1}{{{k}_{3}}}...$ However, case may also arise in which both series and parallel combination is given.