Let T_(1)" and "T_(2) be the time periods of spring A and B when mass M is suspended from theend of the spring. If both springs are taken in series and the same mass M is suspended from the series combination, the time period is T, then

Let T_(1)" and "T_(2) be the time periods of spring A and B when mass

1.	Let T_(1)" and "T_(2) be the time periods of spring A and B when mass M is suspended from theend of the spring. If both springs are taken in series and the same mass M is suspended from the series combination, the time period is T, then
Answer» `T= T_(1) +T_(2)` `(1)/(T) = (1)/(T_1) +(1)/(T_2)` `T^(2)= T_(1)^(2) +T_(2)^(2)` `(1)/(T^2) = (1)/(T_(1)^(2)) +(1)/(T_(2)^(2))` SOLUTION :From `T= 2pi sqrt((M)/(K)), k= (4PI^(2) M)/(T)` `THEREFORE k_(1)= (4pi^(2)M)/(T_(1)^(2))" and "k_(2)= (4pi^(2)M)/(T_(2)^(2))` For series combination, `(1)/(k)=(1)/(k_1)+(1)/(k_2)= (T_(1)^(2))/(4pi^(2)M)+(T_(2)^(2))/(4pi^(2)M)= (T_(1)^(2)+T_(2)^(2))/(4pi^(2)M)` `therefore k= (4pi^(2)M)/(T_(1)^(2)+T_(2)^(2))` `therefore T_(1)^(2)+ T_(2)^(2)= 4pi^(2) (M)/(k)` `therefore sqrt(T_(1)^(2)+T_(2)^(2))= 2pi sqrt((M)/(k))` is the resultant periodic time.