Question 351: Oscillations

Question

Two bodies $A$ and $B$ of equal mass are suspended from two separate massles springs of force constant $k_1$ and $k_2$, 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

Accepted Answer

The maximum velocity of body in SHM,
$$v=A \omega$$
where, $A$ is amplitude of body and $\omega$ is the angulat frequency.
It is given that, the maximum velocities of bodies are equal.
$$\begin{aligned}
v_A & =v_B \
A_A \omega_A & =A_B \omega_B \
A_A \sqrt{\frac{k_1}{m}} & =A_B \sqrt{\frac{k_2}{m}} \quad\left(\because \omega=\sqrt{\frac{k}{m}}ight) \
\frac{A_A}{A_B} & =\sqrt{\frac{k_2}{k_1}}
\end{aligned}$$

Answer

$\sqrt{\frac{k_2}{k_1}}$

Answer

$\frac{k_2}{k_1}$

Answer

$\frac{k_1}{k_2}$

Answer

$\sqrt{\frac{k_1}{k_2}}$

Oscillations

Two bodies A and B of equal mass are suspended from two separate massles springs of force constant k_1 and k_2, 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

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