Two springs have spring constants ${K_A}$ and ${K_B}$ and ${K_A} > {K_B}$. The work required to stretch them by same extension 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

A mass attached to a spring is free to oscillate, with angular velocity $\omega,$ in a hortzontal plane without friction or damping. It is pulled to a distance $x_{0}$ and pushed towards the centre with a velocity $v_{ o }$ at time $t=0 .$ Determine the amplitude of the resulting oscillations in terms of the parameters $\omega, x_{0}$ and $v_{ o } .$ [Hint: Start with the equation $x=a \cos (\omega t+\theta)$ and note that the initial velocity is negative.]

Aheavy brass sphere is hung from a light spring and is set in vertical small oscillation with a period $T.$ The sphere is now immersed in a non-viscous liquid with a density $1/10\,th$ the density of the sphere. If the system is now set in vertical $S.H.M.,$ its period will be

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

Maximum amplitude(in $cm$) of $SHM$ so block A will not slip on block $B , K =100 N / m$