Initially spring is in natural length and both blocks are in rest condition. Then determine Maximum extension is spring. $k=20 N / M$

The potential energy of a weight less spring compressed by a distance $ a $ is proportional to

Two block of masses $m_1$ and $m_2$ connected with the help of a spring of spring constant $k$ initially to natural length as shown. A sharp impulse is given to mass $m_2$ so that it acquires a velocity $v_0$ towards right. If the system is kept an smooth floor then find the maximum elongation that the spring will suffer

A block $(B)$ is attached to two unstretched springs $\mathrm{S} 1$ and $\mathrm{S} 2$ with spring constants $\mathrm{k}$ and $4 \mathrm{k}$, respectively (see figure $\mathrm{I}$ ). The other ends are attached to identical supports $M1$ and $M2$ not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block $\mathrm{B}$ is displaced towards wall $1$ by a small distance $\mathrm{x}$ (figure $II$) and released. The block returns and moves a maximum distance $\mathrm{y}$ towards wall $2$ . Displacements $\mathrm{x}$ and $\mathrm{y}$ are measured with respect to the equilibrium position of the block $B$. The ratio $\frac{y}{x}$ is Figure: $Image$

A chain of mass $m$ and length $l$ is hanging freely from edge $A$ (as shown in diagram $I$ ). Calculate the work done to fold it as shown in diagram $(II)$ 

A spring of force constant $k$ is cut into three equal pieces. If these three pieces are connected in parallel the force constant of the combination will be