A mass $m$ is attached to two springs as shown in figure. The spring constants of two springs are $K _1$ and $K _2$. For the frictionless surface, the time period of oscillation of mass $m$ is
$\frac{1}{2 \pi} \sqrt{\frac{ K _1+ K _2}{ m }}$
$\frac{1}{2 \pi} \sqrt{\frac{ K _1- K _2}{ m }}$
$2 \pi \sqrt{\frac{ m }{ K _1+ K _2}}$
$2 \pi \sqrt{\frac{m}{K_1-K_2}}$
A particle of mass $m$ is performing linear simple harmonic motion. Its equilibrium is at $x = 0,$ force constant is $K$ and amplitude of $SHM$ is $A$. The maximum power supplied by the restoring force to the particle during $SHM$ will be
Infinite springs with force constant $k$, $2k$, $4k$ and $8k$.... respectively are connected in series. The effective force constant of the spring will be
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
Two springs of force constants $300\, N / m$ (Spring $A$) and $400$ $N / m$ (Spring $B$ ) are joined together in series. The combination is compressed by $8.75\, cm .$ The ratio of energy stored in $A$ and $B$ is $\frac{E_{A}}{E_{B}} .$ Then $\frac{E_{A}}{E_{B}}$ is equal to
A uniform stick of mass $M$ and length $L$ is pivoted at its centre. Its ends are tied to two springs each of force constant $K$ . In the position shown in figure, the strings are in their natural length. When the stick is displaced through a small angle $\theta $ and released. The stick