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
$\frac{{{K^{\frac{3}{2}}}{A^2}}}{{\sqrt m }}$
$\frac{{2{K^{\frac{3}{2}}}{A^2}}}{{\sqrt m }}$
$\frac{{{K^{\frac{3}{2}}}{A^2}}}{{3\sqrt m }}$
$\frac{{{K^{\frac{3}{2}}}{A^2}}}{{2\sqrt m }}$
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
A block $P$ of mass $m$ is placed on a smooth horizontal surface. A block $Q$ of same mass is placed over the block $P$ and the coefficient of static friction between them is ${\mu _S}$. A spring of spring constant $K$ is attached to block $Q$. The blocks are displaced together to a distance $A$ and released. The upper block oscillates without slipping over the lower block. The maximum frictional force between the block is
A body executes simple harmonic motion under the action of a force $F_1$ with a time period $(4/5)\, sec$. If the force is changed to $F_2$ it executes $SHM$ with time period $(3/5)\, sec$. If both the forces $F_1$ and $F_2$ act simultaneously in the same direction on the body, its time period (in $seconds$ ) is
Two springs having spring constant $k_1$ and $k_2$ is connected in series, its resultant spring constant will be $2\,unit$. Now if they connected in parallel its resultant spring constant will be $9\,unit$, then find the value of $k_1$ and $k_2$.
A block of mass $2\,kg$ is attached with two identical springs of spring constant $20\,N / m$ each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position, it executes a simple harmonic motion. The time period of oscillation is $\frac{\pi}{\sqrt{x}}$ in SI unit. The value of $x$ is $..........$