Question

An object of mass of 2. 0 kg hangs from an ideal massless spring with a spring constant of 50 N/m. An oscillating force F = (4. 8 N) cos[(3. 0 rad/s)t] is applied to the object. What is the amplitude of the resulting oscillations? You can neglect damping.

A) 0. 15 m

B) 0. 30 m

C) 1. 6 m

D) 2. 4 m

E) 0. 80 m

Answer 1

The amplitude of the resulting oscillations is 4.8 N.

Step-by-step explanation:

To find the amplitude of the resulting oscillations, we need to determine the maximum force exerted by the oscillating force. Since the force is given by F = (4.8 N) cos[(3.0 rad/s)t], we can find the maximum force by taking the absolute value of the coefficient of the cosine term, which is 4.8 N. In this case, the maximum force is equal to the amplitude of the oscillations. Therefore, the amplitude of the resulting oscillations is 4.8 N.

Answer 2

The amplitude of the resulting oscillations can be calculated using the formula:

A = F/mω^2

where F is the amplitude of the applied force, m is the mass of the object, and ω is the angular frequency of the applied force.

In this case, F = 4.8 N, m = 2.0 kg, and ω = 3.0 rad/s.

Substituting these values into the formula, we get:

A = 4.8/(2.0 x (3.0)^2) = 0.267 m or 0.27 m (rounded to two significant figures)

Therefore, the amplitude of the resulting oscillations is 0.27 m, which is closest to option A) 0.15 m.

Step-by-step explanation: