When a mass $m$ is attached to a spring,it normally extends by $0.2\, m$. If the mass $m$ is given a slight additional extension and released,what will be its time period?

In the given figure,a mass $M$ is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is $k$. The mass oscillates on a frictionless surface with time period $T$ and amplitude $A$. When the mass is at its maximum displacement (extreme position),another mass $m$ is gently placed upon it. The new amplitude of oscillation will be

$A$ spring-mass system is oscillating horizontally. What will be the effect on the time period if the spring is made to oscillate vertically?

Two identical springs of spring constant $k$ are attached to a block of mass $m$ and to fixed supports as shown in the figure. When the mass is displaced from the equilibrium position by a distance $x$ towards the right,find the restoring force.

$A$ block of mass $m$ is suspended separately by two different springs having time periods $t_1$ and $t_2$. If the same mass is connected to a parallel combination of both springs,then its time period will be

$A$ spring has a certain mass suspended from it and its period of 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 of $T_2 / T_1$ is