MHT CET20255 May 2025Evening ShiftPhysicsOscillationsActual
All the springs in fig. (a), (b) and (c) are identical, each having force constant K each. Mass m is attached to each system. If T_a, T_b and T_c are the time periods of oscillations of the three systems in fig. (a), (b) and (c) respectively, then
Options
- AT _ a = 2 ~T _ b
- BT _ a = T _ c 2
- CT _ b =2 ~T _ a
- DT _ b =2 ~T _ c
Correct answer
D. T _ b =2 ~T _ c
Step-by-step solution
The time period for a spring-mass system is given by T = 2 m / K_ eq , where m is the mass and K_ eq is the equivalent spring constant. System (a): With one spring of constant K , K_ eq ,a = K and T_a = 2 m / K . System (b): Two springs in series yield 1 / K_ eq ,b = 1 / K + 1 / K = 2 / K , so K_ eq ,b = K / 2 and T_b = 2 2m / K = 2 , T_a . System (c): Two springs in parallel yield K_ eq ,c = K + K = 2K , so T_c = 2 m / (2K) = T_a / 2 . Evaluating the options: Option A: T_a = 2 , T_b gives T_a = 2 ( 2 , T_a) = 2 T_