Write the formula for the time period $(T)$ of a particle executing Simple Harmonic Motion $(SHM)$.

As shown in the figure,a spring with spring constant $k = 150 \ N/m$ is kept in a stretched position by holding two masses of $1 \ kg$ and $200 \ g$ at a separation greater than the natural length of the spring. When the masses are released,assuming the horizontal surface to be frictionless,the angular frequency (in $SI$ units) of the system is:

$A$ spring has a certain mass suspended from it and its period for vertical oscillations is $T_1$. The spring is now cut into two equal halves and the same mass is suspended from one of the halves. The period of vertical oscillations is now $T_2$. The ratio $T_1 / T_2$ is

$A$ vertical spring oscillates with a period of $6 \ s$ when a mass $m$ is suspended from it. When the mass is at rest,the spring is stretched through a distance of (Take acceleration due to gravity $g = \pi^2 = 10 \ m/s^2$): (in $m$)

The restoring force of a spring with a block attached to the free end of the spring is represented 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.