A vertical scale on a spring balance reads from 0 to 160 N T

A vertical scale on a spring balance reads from 0 to 160 N. The scale has a length of 11.0 cm from the 0 to 160 N reading. A fish hanging from the bottom of the spring oscillates vertically at a frequency of 3.00 Hz. Ignoring the mass of the spring, what is the mass m of the fish? Express your answer in kilograms.

Solution

here,
length of scale, L = 11 cm = 0.11 m

frequency of oscillation, f = 3 Hz

time peroid of spring, t = 1/f =1/3 = 0.333 s

Spring constant, k = f/L = 160/0.11 = 1454.545 N/m

since f = (1/2pi)*sqrt(K/m)

solving for mass of fish ,m:
m = k/(2*pi*f)^2
m = 1454.454/(2*pi*3)^2
m = 4.094 kg