Answer:
39.7 N/m
Explanation:
You want to know the spring constant in a spring-mass system in which a 125 N object vibrates with a period of 3.56 s.
Period
The period of a spring-mass system is given by ...
T = 2π√(m/k)
Solving for k, we find ...
(T/(2π))² = m/k
k = m(2π/T)² = (F/g)(2π/T)²
k = (125/9.8)(2π/3.56)² ≈ 39.7 . . . . . . N/m
The spring constant is about 39.7 N/m.
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Additional comment
This means the spring is stretched about 3.14 m at its equilibrium position.
