The mass attached to the spring must be 0.72 kg
Explanation:
The frequency of vibration of a spring-mass system is given by:
(1)
where
k is the spring constant
m is the mass attached to the spring
We can find the spring constant by using Hookes' law:
where
F is the force applied on the spring
x is the stretching of the spring
When a mass of m = 2.82 kg is applied to the spring, the force applied is the weight of the mass, so we have
and using and
, we find
Now we want the frequency of vibration to be
f = 7.42 Hz
So we can rearrange eq.(1) to find the mass m that we need to attach to the spring:
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