$A$ spring has a certain mass suspended from it and its period for vertical oscillation is $T$. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillation is now

$A$ block of mass $M$ hangs from a spring and oscillates vertically with an angular frequency $\omega$. If the block is removed from the spring,when it is in equilibrium position,the spring shortens by

One end of a long metallic wire of length $L$,area of cross-section $A$,and Young's modulus $Y$ is tied to the ceiling. The other end is tied to a massless spring of force constant $K$. $A$ mass $m$ hangs freely from the free end of the spring. It is slightly pulled down and released. Its time period is given by

$A$ $5\; kg$ collar is attached to a spring of spring constant $500\; N m^{-1}$. It slides without friction over a horizontal rod. The collar is displaced from its equilibrium position by $10.0\; cm$ and released. Calculate
$(a)$ the period of oscillation.
$(b)$ the maximum speed and
$(c)$ maximum acceleration of the collar.

Two bodies of masses $1\, kg$ and $4\, kg$ are connected to a vertical spring,as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency $25\, rad/s$,and amplitude $1.6\, cm$ while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is ..... $N$ (take $g = 10\, m/s^2$).

$A$ $2\, kg$ block moving with $10\, m/s$ strikes a spring of constant $\pi^2\, N/m$ attached to a $2\, kg$ block at rest kept on a smooth floor. The time for which the moving block remains in contact with the spring will be ... $\sec$.