Two springs having spring constant $k_1$ and $k_2$ is connected in series, its resultant spring constant will be $2\,unit$. Now if they connected in parallel its resultant spring constant will be $9\,unit$, then find the value of $k_1$ and $k_2$.

A $1\,kg$ mass is attached to a spring of force constant $600\,N / m$ and rests on a smooth horizontal surface with other end of the spring tied to wall as shown in figure. A second mass of $0.5\,kg$ slides along the surface towards the first at $3\,m / s$. If the masses make a perfectly inelastic collision, then find amplitude and time period of oscillation of combined mass.

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. So, the frequency of vibration of the $8\, kg$ block is ….. $Hz$

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

A block of mass $m$ is attached to two springs of spring constants $k_1$ and $k_2$ as shown in figure. The block is displaced by $x$ towards right and released. The velocity of the block when it is at $x/2$ will be