The frequency of oscillations of a mass m suspended by spring is v_(1). If the length of the spring is cut to one- third, the same mass oscillates with frequency v_(2). Determine the value of (v_(2))/(v_(1)).

The frequency of oscillations of a mass m suspended by spring is v_(1)

1.	The frequency of oscillations of a mass m suspended by spring is v_(1). If the length of the spring is cut to one- third, the same mass oscillates with frequency v_(2). Determine the value of (v_(2))/(v_(1)).
Answer» SOLUTION :Let k be the spring constant of FULL spring. Then, `v_(1)=(1)/(2pi) sqrt((k)/(m)) ""....(1)` When the spring is cut one- thirdd of its LENGTH, its spring constant k=3k. Now `v_(2)=(1)/(2pi) sqrt((k')/(m))` `=(1)/(2pi) sqrt((3k)/(m))` `:. (v_(2))/(v_(1))= sqrt(3)`