A mass of 0.40 kg is attached to a spring and
is set into vibration with a period of 0.15 s.
What is the spring constant of the spring?
Answer in units of N/m
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To find the spring constant of the spring, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.
The formula for the period of a mass-spring system is given by:
T = 2π √(m / k)
Where:
T = period of vibration (0.15 s in this case)
m = mass (0.40 kg)
k = spring constant (to be determined)
Rearranging the formula, we have:
k = (4π²m) / T²
Now, we can substitute the given values into the formula and solve for k:
k = (4π² * 0.40 kg) / (0.15 s)²
k ≈ 1666.67 N/m
Therefore, the spring constant of the spring is approximately 1666.67 N/m.