A mass $M$, attached to a horizontal spring, executes s.h.m. with amplitude $A_1$. When the mass $M$ passes through its mean position then a smaller mass $m$ is placed over it and both of them move together with amplitude $A_2$. The ratio of $\left(\frac{A_1}{A_2}\right)$ is
 

Two identical springs are connected to a mass $m$ as shown in Fig. 22.67 ($k=$spring constant). If the period of the configuration in (a) is $2 \mathrm{s}$, the period of the configuration in (b) is

Two springs are joined and attached to a mass of $16 \mathrm{kg}$. This system is then suspended vertically from a rigid support. The spring constant of the springs are $k_1$ and $k_2$ respectively. The period of vertical oscillations of the system will be

Two springs, of force constants $k_1$ and $k_2$ are connected to a mass $m$ as shown in Fig. 22.68. The frequency of oscillation of mass is $f$. If both $k_1$ and $k_2$ are made four times their original values, the frequency of oscillation becomes

A spring (spring constant $=k$) is cut into $4$ equal parts and two parts are connected in parallel. What is the effective spring constant?

A mass of $2.0 \mathrm{kg}$ is put on a flat pan attached to a vertical spring fixed on the ground as shown in Figure. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes a simple harmonic motion. The spring constant is $200 {\mathrm{Nm}}^{-1}$. What should be the minimum amplitude of the motion, so that the mass gets detached from the pan? Take $\mathrm{g}=10 \mathrm{m}/{\mathrm{s}}^2$