A mass $m$ is suspended from a spring of force constant $k$ and just touches another identical spring fixed to the floor as shown in the figure. The time period of small oscillations is
$2 \pi \sqrt{\frac{ m }{ k }}$
$\pi \sqrt{\frac{ m }{ k }}+\pi \sqrt{\frac{ m }{ k / 2}}$
$\pi \sqrt{\frac{ m }{3 k / 2}}$
$\pi \sqrt{\frac{ m }{ k }}+\pi \sqrt{\frac{ m }{2 k }}$
A mass $m$ is suspended from the two coupled springs connected in series. The force constant for springs are ${K_1}$ and ${K_2}$. The time period of the suspended mass will be
What is the period of small oscillations of the block of mass $m$ if the springs are ideal and pulleys are massless ?
On a smooth inclined plane, a body of mass $M$ is attached between two springs. The other ends of the springs are fixed to firm supports. If each spring has force constant $K$, the period of oscillation of the body (assuming the springs as massless) is
In the adjacent figure, if the incline plane is smooth and the springs are identical, then the period of oscillation of this body is
In the figure shown, there is friction between the blocks $P$ and $Q$ but the contact between the block $Q$ and lower surface is frictionless. Initially the block $Q$ with block $P$ over it lies at $x=0$, with spring at its natural length. The block $Q$ is pulled to right and then released. As the spring - blocks system undergoes $S.H.M.$ with amplitude $A$, the block $P$ tends to slip over $Q . P$ is more likely to slip at