Question

A circular spring of stiffness constant k = 30 N/m is cut and and then welded with two blocks of masses 2 kg and 4 kg such that ratio of length of spring between the blocks is 1 : 3 The angular frequency of oscillation of blocks in a smooth horizontal rigid tube if the blocks are slightly displaced form equilibrium position is

• A. $\sqrt{\frac{80}{3}}rad/sec$
• B. $\sqrt{120}rad/sec$
• C. $\sqrt{\frac{40}{3}}rad/sec$
• D. $\sqrt{60}rad/sec$

Answer 1

The correct option is B $\sqrt{120}rad/sec$

$K_1\frac{l}{4}=k_2\frac{3l}{4}=kl$

$K_1=4k,K_2=\frac{4k}{3}$

$\mu =\frac{m_1{m}_2}{m_1{m}_2}=\frac{4}{3}$

$\omega =\sqrt{\frac{K_{eq}}{\mu }}=\sqrt{120}rad/sec$