A simple harmonic oscillator consists of an object on a spring,with the whole of the apparatus in a vat of fluid.If the damping constant is exactly one tenth that required for critical damping,what is the ratio of the damped period to the oscillator's period if set in motion outside the vat of fluid?
A)1.005
B)1.000
C)0.995
D)0.949
E)More information is needed.

Question

Quizplus · Accepted Answer

The ratio of the damped period to the oscillator's period, denoted by "R", can be calculated using the following formula: R = sqrt(1 - (c/2w)^2), where "c" is the damping constant and "w" is the natural frequency of the oscillator. When the damping constant is one-tenth that required for critical damping, it means that c = (1/10) * 2mw = (1/5) * mw, where "m" is the mass of the object. Thus, we have: 
R = sqrt(1 - ((1/5) * m * w / 2w)^2) = sqrt(1 - (1/100)) = sqrt(99/100) = 0.995. 
Therefore, the correct answer is (C).

A Simple Harmonic Oscillator Consists of an Object on a Spring,with