Arrive at the expression for time period of oscillation of a mass attached to a vertical spring.

Explanation

Consider a spring of force constant k. Let a mass body .m. be at one end of the massless spring. Let the other end of the spring be supported vertically.
Force `=-kx=ma`
hence`" "ma+kx =0`
`"i.e. "m(d^(2)x)/(dt^(2))+kx=0`
`"or "(d^(2)x)/(dt^(2))+((k)/(m))x=0`
Compaaring (1) with a standard diffential equation `(d^(2)x)/(dt^(2))+omega^(2)x=0` representing S.H.M we write
angular frequency `omega^(2)=(k)/(m)`
or `omega=sqrt((k)/(m)) or (2pi)/(T)=sqrt((k)/(m))`
`therefore" period of oscillation T"=2pisqrt((m)/(k))`.
where, `k-`is the spring constant.