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

Arrive at the expression for time period of oscillation of a mass atta

1.	Arrive at the expression for time period of oscillation of a mass attached to avertical spring.
Answer» Solution :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.