The effective spring constant of the two-spring system as shown in the figure will be:

Two massless springs of force constants $K_1$ and $K_2$ are joined end to end. The resultant force constant $K$ of the system is

In the given arrangement,the spring constant $k$ has a value of $2\,N\,m^{-1}$,mass $M = 3\,kg$,and mass $m = 1\,kg$. Mass $M$ is in contact with a smooth surface. The coefficient of friction between the two blocks is $0.1$. The time period of $SHM$ executed by the system is

Three masses $700 \, g, 500 \, g$,and $400 \, g$ are suspended at the end of a spring as shown and are in equilibrium. When the $700 \, g$ mass is removed,the system oscillates with a period of $3 \, s$. When the $500 \, g$ mass is also removed,it will oscillate with a period of ...... $s$.

$A$ block is fastened to a horizontal spring. The block is pulled to a distance $x = 10 \text{ cm}$ from its equilibrium position (at $x = 0$) on a frictionless surface from rest. The kinetic energy of the block at $x = 5 \text{ cm}$ is $0.25 \text{ J}$. The spring constant of the spring is nearly (in $\text{Nm}^{-1}$)

$A$ particle of mass $m$ in a unidirectional potential field has potential energy $U(x) = \alpha + 2 \beta x^2$,where $\alpha$ and $\beta$ are positive constants. Find its time period of oscillation.