Finding frecuency??an elastic cord vibrates

An elastic cord vibrates with a frequency of 3.2 Hz when a mass of 0.55 kg is hung from it. What will its frequency be if only 0.38 kg hangs from it?

Imagine the string is like a spring, then you can use Hooke's law to model its vibration and assign it a spring constant k. The relationship between the spring constant (k), the mass of the object hanging from the spring (m) and the oscillation frequency (f) in Hertz, is then given by

2*pi*f = sqrt(k/m)

so if you know that for m = 0.55 kg you observe f = 3.2 Hz, this means that

2*pi*3.2 = sqrt(k/0.55)

and thus solving for k we get

k = 0.55*(2*pi*3.2)^2 = 222.342 (N/m)

now that we know k if they tell us that the mass is changed to 0.38 kg, then we can calculate the new oscillation frequency from

2*pi*f = sqrt(k/m)

by solving for f

f = 1/(2*pi) * sqrt(k/m)

and plugging in for k and m

f = 1/(2*pi) * sqrt(k/m) = 1/(2*pi) * sqrt(222.342/0.38) = 3.84981 Hz