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.
-The oscillation is
A)very weakly damped.
B)weakly damped.
C)critically damped.
D)overdamped.
E)unable to tell

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. 
-The oscillation is
A)very weakly damped. 
B)weakly damped. 
C)critically damped. 
D)overdamped. 
E)unable to tell

Quizplus · Accepted Answer

Based on the given values of mass, radius, spring constant, and viscosity, we can calculate the critical damping coefficient as:
c = 2m√kr = 0.4 Ns/m
The damping coefficient of the ball immersed in oil is given by:
c' = 4πrη = 3.14 Ns/m
Since c' > c, the oscillation is weakly damped.

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