Discussion Forum

Two bodies  A and B of equal mass are suspended from two separate massless springs of force constant k₁ and k₂, respectively. The bodies oscillate vertically such that their maximum velocities are equal. The ratio of the amplitudes  of body  A to that of body B is 

Answer:

Explanation:

 The maximum velocity of body in SHM

                                   v= A $\omega$

 where , A is amplitude  of body and $\omega$  is the angular frequency.

 It is given that , the maximum velocities of bodies are equal

                       $V_{A}=V_{B}$

 $A_{A}\omega_{A}=A_{B}\omega_{B}$

 $A_{A}\sqrt{\frac{k_{1}}{m}}=A_{B}\sqrt{\frac{k_{2}}{m}}$           

                                                                                    $\left(\because \omega =\sqrt{\frac{k}{m}}\right)$

 $\frac{A_{A}}{A_{B}}=\sqrt{\frac{k_{2}}{k_{1}}}$