Suppose a 2662 kg giant seal is placed on a scale and produces a 20.0 cm compres-
sion. If the seal and spring system are set into simple harmonic motion, what is
the period of the oscillations?
First, we need to calculate the spring constant (k) from the compression distance and the weight of the seal.
The force exerted by the seal on the spring can be calculated using Hooke's Law:
F = kx
where F is the force, k is the spring constant, and x is the compression distance.
The weight of the seal can be converted to force using:
F = mg
where F is the force, m is the mass, and g is the acceleration due to gravity (9.81 m/s^2).
Substitute the above equations:
kx = mg
k = mg/x
k = (2662 kg)(9.81 m/s^2)/(0.20 m)
k ≈ 130445 N/m
Next, we can calculate the period of the oscillations using the formula:
T = 2π√(m/k)
T = 2π√(2662 kg/130445 N/m)
T ≈ 0.366 s
Therefore, the period of the oscillations is approximately 0.366 seconds.