Damped harmonic motion: A 25 kg object is undergoing lightly damped harmonic oscillations. If the maximum displacement of the object from its equilibrium point drops to 1/3 its original value in 1.8 s, what is the value of the damping constant b?
A) 31 kg/s
B) 34 kg/s
C) 37 kg/s
D) 40 kg/s

Question

Quizplus · Accepted Answer

The damping constant b can be calculated using the formula for damped harmonic motion: $ x(t) = x_0 e^{-\frac{b}{2m}t} $. Given that the displacement drops to 1/3 its original value in 1.8 s, we can solve for b: $ \frac{1}{3} = e^{-\frac{b}{2 \times 25} \times 1.8} $. Solving this equation gives b ≈ 31 kg/s.

Damped Harmonic Motion: a 25 Kg Object Is Undergoing Lightly