On the arrangement shown in figure Pulleys are small light and springs are ideal K_1 , K_2 , K_3 and K_4 are force constant of the springs calculate period of small vertical oscillations of block of mass 'm'

On the arrangement shown in figure Pulleys are small light and springs

1.	On the arrangement shown in figure Pulleys are small light and springs are ideal K_1 , K_2 , K_3 and K_4 are force constant of the springs calculate period of small vertical oscillations of block of mass 'm'
Answer» Solution :If the BLOCK is pulled down by a SMALL displacement x and RELEASED , extra tension provides restoring force Let T be the extra tension Then T = ma If `x_1 , x_2 , x_3 and x_4` are the extensions of springs. `2T = K_1 x_1 = K_2x_2 = K_3 x_3= K_4 x_4` `x=2(x_1 + x_2 + x_3+x_4)` `x= 4T (1/(K_1) + 1/(K_2) + 1/(K_3) + 1/(K_4))` from T = ma `4m(1/(K_1) + 1/(K_2) + 1/(K_3) + 1/(K_4)) a= x , omega = SQRT(a/x) and T = (2pi)/(omega)`