Find the natural frequency of oscillation of the system as shown in figure. Pulleys are massless and frictionless. Spring and string are also massless. (Take `pi^(2)=10`)

Options

A. `(pi)/2 Hz`
B. `sqrt(pi) Hz`
C. `10/(sqrt(pi))Hz`
D. `pi Hz`

Explanation

Let mass 'm' falls down by x so spring extends by 4x ,
`:. T/4=k(4x)`
T=(16 k)x
Where T is the restoring force on mass m
`:. F=1/(2pi)sqrt((16 k)/m)`
`f=2/(pi)sqrt(k/m)=2/(pi)xxsqrt(25/1)=pi Hz`