$A$ weightless spring which has a force constant $k$ oscillates with frequency $n$ when a mass $m$ is suspended from it. The spring is cut into two equal halves and a mass $2m$ is suspended from one of the halves. The frequency of oscillation will now become:

$A$ 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 $m$)

Figure $(a)$ shows a spring of force constant $k$ clamped rigidly at one end and a mass $m$ attached to its free end. $A$ force $F$ applied at the free end stretches the spring. Figure $(b)$ shows the same spring with both ends free and attached to a mass $m$ at either end. Each end of the spring in Figure $(b)$ is stretched by the same force $F$.
$(a)$ What is the maximum extension of the spring in the two cases?
$(b)$ If the mass in Figure $(a)$ and the two masses in Figure $(b)$ are released,what is the period of oscillation in each case?

$A$ mass at the end of a spring executes harmonic motion about an equilibrium position with an amplitude $A$. Its speed as it passes through the equilibrium position is $V$. If extended $2A$ and released,the speed of the mass passing through the equilibrium position will be

$A$ spring of force constant $k$ is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force constant of

$A$ mass $M$ is suspended from a light spring. An additional mass $m$ added displaces the spring further by a distance $x$. Now the combined mass will oscillate on the spring with period