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 $\frac{E_A}{E_B}$. Then $\frac{E_A}{E_B}$ is equal to

$A$ $1 \, kg$ block attached to a spring vibrates with a frequency of $1 \, Hz$ on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an $8 \, kg$ block placed on the same table. The frequency of vibration of the $8 \, kg$ block is ..... $Hz$.

$A$ particle at the end of a spring executes simple harmonic motion with a period $t_1$,while the corresponding period for another spring is $t_2$. If the period of oscillation with the two springs in series is $T$,then

$A$ block $P$ of mass $m$ is placed on a smooth horizontal surface. $A$ block $Q$ of same mass is placed over the block $P$ and the coefficient of static friction between them is $\mu_S$. $A$ spring of spring constant $K$ is attached to block $Q$. The blocks are displaced together to a distance $A$ and released. The upper block oscillates without slipping over the lower block. The maximum frictional force between the blocks is

The period of oscillation of a mass $M$ suspended from a spring of negligible mass is $T$. If along with it another mass $M$ is also suspended,the period of oscillation will now be

The equivalent spring constant of the system as shown in the figure will be: