The time the spring be 2 ft high is 25.7 seconds
Since the spring is oscillating vertically according to the equation y = 3cos(2t – π), where y is the displacement in feet and t is time in seconds.
We need to find the time when the spring is 2 ft high. So, y = 2.
Since y = 3cos(2t – π)
Making t subject of the formula, we have
y/3 = cos(2t – π)
2t – π = cos⁻¹(y/3)
2t = π + cos⁻¹(y/3)
t = [π + cos⁻¹(y/3)]/2
Substituing y = 2 into the equation, we have
t = [π + cos⁻¹(y/3)]/2
t = [π + cos⁻¹(2/3)]/2
t = [π + cos⁻¹(0.666)]/2
t = [π + 48.19]/2
t = [3.142 + 48.19]/2
t = 51.332/2
t = 25.67
t ≅ 25.7 seconds
The time the spring be 2 ft high is 25.7 seconds
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