Use the figure to the right to answer the next problem. A ball of mass m = 100 g and radius r = 10 cm is suspended from a light spring with spring constant k = 4 N / m.The ball is then immersed in oil with viscosity = 0.2 Pa.s , and set into oscillation with an initial amplitude of A = 2 cm.
-What is the angular frequency of oscillation?
A)6.32 rad/s
B)7.23 rad/s
C)6.03 rad/s
D)4.15 rad/s
E)3.16 rad/s

Question

Use the figure to the right to answer the next problem. A ball of mass m = 100 g and radius r = 10 cm is suspended from a light spring with spring constant k = 4 N / m.The ball is then immersed in oil with viscosity = 0.2 Pa.s , and set into oscillation with an initial amplitude of A = 2 cm. 
-What is the angular frequency of oscillation?
A)6.32 rad/s 
B)7.23 rad/s 
C)6.03 rad/s 
D)4.15 rad/s 
E)3.16 rad/s

Quizplus · Accepted Answer

The angular frequency of oscillation, ω, can be found using the formula
ω = √(k/m - (γ/2m)^2)
where k is the spring constant, m is the mass of the ball, and γ is the damping coefficient given by γ = 6πηr.

Given that k = 4 N/m, m = 0.1 kg, r = 0.1 m, and η = 0.2 Pa.s, we have
γ = 6π(0.2)(0.1) = 0.377 Ns/m

Substituting these values in the formula, we get
ω = √(4/0.1 - (0.377/2*0.1)^2) = 6.03 rad/s

Therefore, the correct answer is C, 6.03 rad/s.

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