A mass of 2.0 kg hangs from a spring with a force constant of 50 N/m. An oscillating force F = (4.8 N) cos[(3.0 rad/s)t] is applied to the mass. What is the amplitude of the resulting oscillations? Neglect damping.
A)0.15 m
B)0.30 m
C)1.6 m
D)2.4 m
E)0.80 m

Question

Quizplus · Accepted Answer

The amplitude of the oscillations can be found using the formula A = F₀ / (m * (ω₀² - ω²)), where F₀ is the force amplitude, m is the mass, ω₀ is the natural frequency, and ω is the driving frequency. Here, ω₀ = sqrt(k/m) = sqrt(50/2) = 5 rad/s, and ω = 3 rad/s. Substituting the values, A = 4.8 / (2 * (5² - 3²)) = 0.15 m.

A Mass of 2