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The natural frequency of oscillation of a mass m attached to a spring with spring constant k is given by f = (1/2*pi)*sqrt(k/m).
When a mass of 21 g is attached to a certain spring, it makes 18 complete vibrations in 3.7 s. This gives the natural frequency of 18/3.7 = 4.864
4.864 = (1/2*pi)*sqrt(k/21*10^-3)
=> k = (4.864*2*pi)^2*21*10^-3 N/m
=> k = 19.62 N/m
The spring constant of a spring that completes 18 oscillations in 3.7 s when a mass of 21 g is attached is 19.62 N/m.
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