An object of mass 0.2kg is hung from a spring whose spring constant is 80N/m. Th

Question

An object of mass 0.2kg is hung from a spring whose spring constant is 80N/m. The object is subject to a resistive force given by -bv where v is its velocity in meters per sec.
A) If the damped frequency is sqrt (3)/2 of the undamped frequency, what is the value of b?
B) What is the Q of the system and by what factor is the amplitude of the oscillation reduced after 10 complete cycles? An object of mass 0.2kg is hung from a spring whose spring constant is 80N/m. The object is subject to a resistive force given by -bv where v is its velocity in meters per sec.
A) If the damped frequency is sqrt (3)/2 of the undamped frequency, what is the value of b?
B) What is the Q of the system and by what factor is the amplitude of the oscillation reduced after 10 complete cycles?
A) If the damped frequency is sqrt (3)/2 of the undamped frequency, what is the value of b?
B) What is the Q of the system and by what factor is the amplitude of the oscillation reduced after 10 complete cycles?

Explanation / Answer

(A) the damping constant,

b = 0.2*1.732*(80/0.2)^0.2

= 6.928

(b) Quality factor = 0.2*80/10 -1 = 1.6-1 = 0.6

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