A block of mass 'm' is tied to one end of string which passes over a smooth pulley 'A' and under a light smooth movable pulley B. The other end of the string is attached to lower end of a string constant K_2. Find the period of small oscillations of mass 'm' about its equilibrium position.

A block of mass 'm' is tied to one end of string which passes over a s

1.	A block of mass 'm' is tied to one end of string which passes over a smooth pulley 'A' and under a light smooth movable pulley B. The other end of the string is attached to lower end of a string constant K_2. Find the period of small oscillations of mass 'm' about its equilibrium position.
Answer» Solution :If the block is pulled down by a small displacement .X. and RELEASED , extra tension provides restoring FORCE Let T be extra tension T= ma If `x_1 and x_2` are the EXTENSIONS of the springs `T= k_2 x_2 and 2T = k_1 x_1 ` `x= 2(x_2 + 2x) = (T)/(k_2) + (2T)/(k_1) = 2T[(k_1 + 2k_2)/(k_1 k_2)]` from T = ma `((k_1 k_2)/(k_1 + 2k_2)) x/2 = ma` `omega = sqrt((k_1 k_2)/(2(k_1 + 2k_2))) m , T= 2pi sqrt((2M(k_1 + 2k_2))/(k_1 k_2))`