A spring of force constant $k$ is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force constant of

If a watch with a wound spring is taken on to the moon, it

A spring is stretched by $5 \,\mathrm{~cm}$ by a force $10 \,\mathrm{~N}$. The time period of the oscillations when a mass of $2 \,\mathrm{~kg}$ is suspended by it is :(in $s$)

The time period of a mass suspended from a spring is $T$. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be

A spring having with a spring constant $1200\; N m ^{-1}$ is mounted on a hortzontal table as shown in Figure A mass of $3 \;kg$ is attached to the free end of the spring. The mass is then pulled sideways to a distance of $2.0 \;cm$ and released. Determine

$(i)$ the frequency of oscillations,

$(ii)$ maximum acceleration of the mass, and

$(iii)$ the maximum speed of the mass.

The graph shown was obtained from experimental measurements of the period of oscillations $T$ for different masses $M$ placed in the scale pan on the lower end of the spring balance. The most likely reason for the line not passing through the origin is that the