A $5\, kg$ collar is attached to a spring of spring constant $500\, Nm^{-1}$. It slides without friction over a horizontal rod. The collar is displaced from its equillibrium position by $10\, cm$ and released. The time period of oscillation is

The drawing shows a top view of a frictionless horizontal surface, where there are two indentical springs with particles of mass $m_1$ and $m_2$ attached to them. Each spring has a spring constant of $1200\  N/m.$ The particles are pulled to the right and then released from the  positions shown in the drawing. How much time passes before the particles are again side by side for the first time if $m_1 = 3.0\  kg$ and $m_2 = 27 \,kg \,?$

Two masses $m_1$ and $m_2$ are supended together by a massless spring of constant $k$. When the masses are in equilibrium, $m_1$ is removed without disturbing the system; the amplitude of vibration is

Two identical springs have the same force constant $73.5 \,Nm ^{-1}$. The elongation produced in each spring in three cases shown in Figure-$1$, Figure-$2$ and Figure-$3$ are $\left(g=9.8 \,ms ^{-2}\right)$

If a spring extends by $x$ on loading, then energy stored by the spring is (if $T$ is the tension in the spring and $K$ is the spring constant)

Two springs, of force constants $k_1$ and $k_2$ are connected to a mass $m$ as shown. The frequency of oscillation of the mass is $f$ If both $k_1$ and $k_2$ are made four times their original values, the frequency of oscillation becomes