Define simple pendulum and the length of pendulum.

Two springs of constant ${k_1}$and ${k_2}$are joined in series. The effective spring constant of the combination is given by

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 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.

In the adjacent figure, if the incline plane is smooth and the springs are identical, then the period of oscillation of this body is