A mass $m$ is suspended by means of two coiled spring which have the same length in unstretched condition as in figure. Their force constant are $k_1$ and $k_2$ respectively. When set into vertical vibrations, the period will be
$2\pi \sqrt {\left( {\frac{m}{{{k_1}{k_2}}}} \right)} $
$2\pi \sqrt {m\left( {\frac{{{k_1}}}{{{k_2}}}} \right)} $
$2\pi \sqrt {\left( {\frac{m}{{{k_1} - {k_2}}}} \right)} $
$2\pi \sqrt {\left( {\frac{m}{{{k_1} + {k_2}}}} \right)} $
A spring with $10$ coils has spring constant $k$. It is exactly cut into two halves, then each of these new springs will have a spring constant
A $2\, Kg$ block moving with $10\, m/s$ strikes a spring of constant $\pi ^2 N/m$ attached to $2\, Kg$ block at rest kept on a smooth floor. The time for which rear moving block remain in contact with spring will be ... $\sec$
The drawing shows a top view of a frictionless horizontal surface, where there are two indentical springs with particles of mass $m_1$ and $m_2$ attached to them. Each spring has a spring constant of $1200\ N/m.$ The particles are pulled to the right and then released from the positions shown in the drawing. How much time passes before the particles are again side by side for the first time if $m_1 = 3.0\ kg$ and $m_2 = 27 \,kg \,?$
A man weighing $60\ kg$ stands on the horizontal platform of a spring balance. The platform starts executing simple harmonic motion of amplitude $0.1\ m$ and frequency $\frac{2}{\pi } Hz$. Which of the following staements is correct
A spring has spring constant $k$ and $l$. If it cut into piece spring in the proportional to $\alpha : \beta : \gamma $ then obtain the spring constant of every piece in term of spring constant of original spring (Here, $\alpha $, $\beta $ and $\gamma $ are integers)