A mass m performs oscillations of period T when hanged by spring of force constant K . If spring is cut in two parts and arranged in parallel and same mass is oscillated by them, then the new time period will be

Explanation

As we know
`T = 2pi sqrt((m)/(k))`
For series combination
spring constant ,br> ` = (1)/(K_(s)) = (1)/(k) + (1)/(k) = (2)/(k)`
`K_(s) = (k)/(2)`
`therefore T_(s) = 2pi sqrt((m)/(k_(s))) = 2pi sqrt((2m)/(k))`
for parallel combination
spring constant ` = K_(p) = k + k = 2k`
`therefore T_(P) = 2pisqrt((m)/(K_(p)))`
` = 2pi sqrt((m)/(2k))`
`(T_(S))/(T_(P)) = 2pi sqrt((2m)/(k)) xx sqrt((2k)/(m)) = 2`