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Find the time period of the oscilltion of mass m in figure a and b. What is the equivalent spring constant of the spring in each case. ?

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In figure (a)
`k_(eq)= (k_(1)k_(2))/(k_(1)+k_(2))+k_(3)=(k_(1)k_(2)+k_(2)k_(3)+k_(1)k_(3))/(k_(1)+k_(2))`
Now `T=2pisqrt((m)/(k_(eq)))=2pisqrt((m(k_(1)+k_(2)))/(k_(1)k_(2)+k_(2)k_(3)+k_(1)k_(3)))`


Case (B )
If the block is displaced slightly by an amount x then both the spring are displaced by x from their natural length so it is parallel combination of springs. which gives
`K_(eq) = k_1 + K_2`
` T= 2pi sqrt((m)/( k_(eq)) = 2 pi sqrt( (m))/( k_(1)+k_(2))`
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