Find the ratio of time periods of two identical springs if they are first joined in series $\&$ then in parallel $\&$ a mass $m$ is suspended from them :

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 spring of force constant $k$ is cut into lengths of ratio $1:2:3$ . They are connected in series and the new force constant is $k'$ . Then they are connected in parallel and force constant is $k''$ . Then $k':k''$ is

What is condition for a body suspended at the end of a spring having simple harmonic oscillation ?

Consider two identical springs each of spring constant $k$ and negligible mass compared to the mass $M$ as shown. Fig. $1$ shows one of them and Fig. $2$ shows their series combination. The ratios of time period of oscillation of the two $SHM$ is $\frac{ T _{ b }}{ T _{ a }}=\sqrt{ x },$ where value of $x$ is

(Round off to the Nearest Integer)

A $100 \,g$ mass stretches a particular spring by $9.8 \,cm$, when suspended vertically from it. ....... $g$ large a mass must be attached to the spring if the period of vibration is to be $6.28 \,s$.