Answer: v = 3.684 m/s
Explanation: The angular frequency (ω) of a loaded spring is given as
ω = √k/m
Where ω = angular frequency, k =spring constant = 11.9 N/m, m = mass of object = 40.1 g = 0.0401 kg.
The velocity of a simple harmonic motion is defied as
v = ω√A² - x²
Where A = Amplitude = 24.7cm = 0.247m and x = displacement.
For our question, we where asked to find velocity at half way, at half way, x = A/2
Hence at half way, x = 0.247/2 = 0.1235 m.
We need to get the value of angular frequency first.
ω = √(11.9/0.0401)
ω = √296.758
ω = 17.22 rad/s.
Then the velocity is
v = 17.22 √0.247² - 0.1235²
v = 17.22 √0.061009 - 0.01525225
v = 17.22 √0.04575675
v = 17.22 × 0.2139
v = 3.684 m/s
