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
$T = 2\pi \sqrt {\left( {mg/x(M + m)} \right)} $
$T = 2\pi \sqrt {\left( {(M + m)x/mg} \right)} $
$T = (\pi /2)\sqrt {\left( {mg/x(M + m)} \right)} $
$T = 2\pi \sqrt {\left( {(M + m)/mgx} \right)} $
When a mass $m$ is attached to a spring, it normally extends by $0.2\, m$. The mass $m$ is given a slight addition extension and released, then its time period will be
If two similar springs each of spring constant $K _{1}$ are joined in series, the new spring constant and time period would be changed by a factor
A spring having a spring constant $‘K’$ is loaded with a mass $‘m’$. The spring is cut into two equal parts and one of these is loaded again with the same mass. The new spring constant is
Two masses $m_1$ and $m_2$ connected by a spring of spring constant $k$ rest on a frictionless surface. If the masses are pulled apart and let go, the time period of oscillation is
An ideal spring with spring-constant $K$ is hung from the ceiling and a block of mass $M$ is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is