• # question_answer 13) Two blocks of masses 1 kg and 3 kg are attached to a horizontal spring of spring constant 300 N/m as shown in the figure. The natural vibrational frequency of the system is, approximately A)  4 Hz                           B)  3 HzC)  2 Hz                           D)  1 Hz

Here, we will use the reduced mass concept, $\mu =\frac{{{m}_{1}}{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}}=\frac{3\times 1}{4}=\frac{3}{4}\,kg.$ The time period of the system $=T=2\pi \sqrt{\frac{\mu }{k}}$ $T=2\pi \sqrt{\frac{3}{4\times 300}}=\frac{2\pi }{20}$ $=\frac{\pi }{10}-\frac{1}{3}s.$ or $f=3\,Hz.$ Hence, the correction option is [b].