Two identical point masses $P$ and $Q$, suspended from two separate massless springs of spring const

Question

Two identical point masses $P$ and $Q$, suspended from two separate massless springs of spring constants $k_1$ and $k_2$, respectively, oscillate vertically. If their maximum speeds are the same, the ratio ( $A_Q / A_P$ ) of the amplitude $A_Q$ of mass $Q$ to the amplitude $A_P$ of mass $P$ is

Professor PC Thomas Classes · Answer

(b) : For a spring-mass system, the angular frequency is given by $ \omega=\sqrt{\frac{k}{m}} $ For body $P: v_{1(\max )}=\omega_1 A_P=\sqrt{\frac{k_1}{m}} A_P$ \ For body \ $Q: v_{2(	ext { max })}=\omega_2 A_Q=\sqrt{\frac{k_2}{m}} A_Q$ \ Equate the equation (i) and (ii), $ \sqrt{\frac{k_1}{m}} A_P=\sqrt{\frac{k_2}{m}} A_Q $ \ or $\sqrt{k_1} A_P=\sqrt{k_2} A_Q$ \ Ratio of the amplitudes of $Q$ and $P$ \ $ \frac{A_Q}{A_P}=\sqrt{\frac{k_1}{k_2}} $