An elastic spring under tension of $3 \mathrm{~N}$ has a lengtha. Its length is $b$ under tension $2 \mathrm{~N}$. For its length$(3 a-2 b)$, the value of tension will be_______. $\mathrm{N}$.

$A$ particle of mass m is constrained to move on $x$ -axis. $A$ force $F$ acts on the particle. $F$ always points toward the position labeled $E$. For example, when the particle is to the left of $E, F$ points to the right. The magnitude of $F$ is a constant $F$ except at point $E$ where it is zero. The system is horizontal. $F$ is the net force acting on the particle. The particle is displaced a distance $A$ towards left from the equilibrium position $E$ and released from rest at $t = 0.$  What is the period of the motion? 

The work done in joules in increasing the extension of a spring of stiffness $10\, N/cm$ from $4\, cm$ to $6\, cm$ is:

Two plates each of mass $m$ are connected by a massless spring as shown below. A weight $w$ is put on the upper plate which compresses the spring further. When $w$ is removed, the entire assembly jumps up. The minimum weight $w$ needed for the assembly to jump up when the weight is removed is just more than ………..$ \,m$

The $P.E.$ of a certain spring when stretched from natural length through a distance $0.3\, m$ is $10\, J$. The amount of work in joule that must be done on this spring to stretch it through an additional distance $0.15\, m$ will be ……………. $\mathrm{J}$