The simple harmonic motion and Hooke's law allows to find the displacement when hanging the mass of 2 kg is:
x = 2.45 m
Simple harmonic motion is a motion where the restoring force is proportional to the displacement.
x = A cos (wt + Ф)
Where x is the displacement, A is the amplitude, w is the angular velocity, t is the time
The angular velocity is
w² = k / m
Where k is the spring constant and m is the mass.
From the graph we see that the oscillatory wave has half a period between the times t₁ = [tex]\frac{3}{4} \pi[/tex] and t₂ = [tex]\frac{1}{4} \pi[/tex] , therefore the period is:
T = π s.
The angle in a complete oscillation is θ = 2π rad.
The angular kinematics defines the angular velocity with the angle in the unit of time.
w = [tex]\frac{\Delta \theta}{\Delta t}[/tex]
w = [tex]\frac{2\pi }{\pi }[/tex]
w = 2 rad / s
Let's find the spring constant.
k = w² m
Let's calculate.
k = 2² 2
k = 8 N / m
Hooke's law says that the restoring force of a spring is proportional to its displacement.
F = - k x
mg = - k x
x = [tex]\frac{mg}{k}[/tex]
x = [tex]\frac{2 \ 9.8}{8}[/tex]
x = 2.45 m
In conclusion using simple harmonic motion and Hooke's law we can find the displacement when hanging the 2kg mass is:
x = 2.45 m
Learn more here: brainly.com/question/17315536
