Answer:
a) T = 1,199 s b) k = 11.0 N / m
Step-by-step explanation:
The oscillatory movement of a mass-spring system is described by the equation
x (t) = A cos (w t)
Where A is the amplitude of the movement. W is the angular velocity, which is given by
w = √ k / m
The amplitude of the system is the maximum elongation that the spring has before releasing it, in this case it is A = 50 cm = 0.50 m, the equation is
x = 0.50 cos (wt)
We can calculate the angular velocity with the point given by x = 0.250 m for t = 0.200s
w t = cos⁻¹ (x / A)
w = 1 / t cos⁻¹ (x / A)
w = 1/0.200 cos⁻¹(0.25 / 0.50)
Let's be careful because the angle is in radians
w = 5.24 rad / s
Angular velocity is
w = 2 π f = 2π / T
T = 2π / w
T = 2π / 5.24
T = 1,199 s
With the angular velocity equation we can take off the spring constant
w² = k / m
k = m w²
k = 0.400 5.24²
k = 11.0 N / m