Two springs of force constants $300 \, N/m$ (Spring $A$) and $400 \, N/m$ (Spring $B$) are joined together in series. The combination is compressed by $8.75 \, cm$. The ratio of energy stored in $A$ and $B$ is $E_A / E_B$. Then $E_A / E_B$ is equal to:

$A$ mass $m$ is suspended from two coupled springs connected in series. The force constants for the springs are $K_1$ and $K_2$. The time period of the suspended mass will be:

If a spring has time period $T$,and is cut into $n$ equal parts,then the time period of each part will be

Two identical springs of spring constant $k$ are attached to a block of mass $m$ and to fixed supports as shown in the figure. Show that when the mass is displaced from its equilibrium position on either side,it executes simple harmonic motion. Find the period of oscillations.

$A$ tray of mass $12 \,kg$ is supported by two identical springs as shown in the figure. When the tray is pressed down slightly and then released, it executes $SHM$ with a time period of $1.5 \,s$. The spring constant of each spring is

$A$ block $P$ of mass $m$ is placed on a frictionless horizontal surface. Another block $Q$ of the same mass $m$ is kept on $P$ and connected to a wall with the help of a spring of spring constant $k$ as shown in the figure. $\mu_s$ is the coefficient of static friction between $P$ and $Q$. The blocks move together performing simple harmonic motion $(SHM)$ of amplitude $A$. The maximum value of the friction force between $P$ and $Q$ is