A block of mass `m` is attached to one end of a light intextensible string passing over a smooth light pulled `A` and under another smooth light pulled `B` as shown in Fig. The other end of a springs is fixed to a ceiling. `A` and `B` are held by spring of force constant `k_(1)` and `k_(2)`. Find the period of small oscillations of system.

Explanation

The given system is equivalent to a system shown in fig Here `K'_(1) = (K_(1))/(4)` and `K'_(2) = (K_(2))/(4)` The equivalent force constant
`K = (K'_(1)K'_(2))/(K'_(1)+K'_(2)) = (K_(1)/(4)xx(K_(2))/(4))/(K_(1)/(4)+K_(1)/(4)) =(K_(1)K_(2))/(4(K_(1)+K_(2)))`
The time period of equivalent system is
`T = 2pi sqrt((m)/(k)) = 2pi sqrt((m)/((k_(1)k_(2))/(4(k_(1)+k_(2))))) = 2pisqrt((4m(k_(1)+k_(2)))/(k_(1)k_(2)))`