Final answer:
The period of oscillation is approximately 2.43 s. The spring constant is 26.23 N/m. The maximum velocity is approximately 1.79 m/s. The displacement at t = 0 is 0.691 m.
Step-by-step explanation:
a) To determine the period of oscillation, we can use the formula:
T = 2π√(m/k)
Where T is the period, m is the mass, and k is the spring constant. In this case, the mass is 4.3 kg and the spring constant can be calculated using the formula:
k = m × a_max
Where a_max is the maximum acceleration. Substituting the values, we get:
k = 4.3 kg × 6.1 m/s² = 26.23 N/m
Now we can calculate the period:
T = 2π√(4.3 kg / 26.23 N/m) ≈ 2.43 s
b) The spring constant is already calculated as 26.23 N/m.
c) The maximum velocity can be found using the formula:
v_max = A × ω
Where A is the amplitude and ω (omega) is the angular frequency given by:
ω = 2π / T
Substituting the values, we get:
ω = 2π / 2.43 s ≈ 2.59 rad/s
and
v_max = 0.691 m × 2.59 rad/s ≈ 1.79 m/s
d) The displacement at t = 0 is equal to the amplitude, which is 0.691 m.