A block of mass M is attached with the springs as shown .If the block is slightly displaced the time period of SHM for the block shown in the figure will be
2π√m9k
2π√mk
4π3√m9k
π√m2k
A
4π3√m9k
B
π√m2k
C
2π√m9k
D
2π√mk
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Solution
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When system moves x units in right then Pulley 1 and Pulley 2 moves xunits in right and required string for each pulley is 2x.
Therefore , both spring are elongated by 2x.
Force exerted=k(2x)
Tension in String(T)=k(2x)
Force exerted by right spring due to x displacement =kx
Net force =2T+2T+kx=9kx
Now net force =mω2x=9kx
Or , ω=√9km
Now time period for SHM=T=2πω=2π√m9k.
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