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Q.

A mass of 2kg oscillates on a spring with force constant 50N/m. By what factor does the frequency of oscillation decreases when a damping force with constant b=12 is introduced?

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a

Decreased by 10%

b

Decreased by 25%

c

Decreased by 50%

d

Decreased by 20%

answer is D.

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Detailed Solution

$W_{0} = \sqrt{\frac{k}{m}} = \sqrt{\frac{50}{2}} = \sqrt{25} = 5 rad/sec$
$r = \frac{b}{2 m} = \frac{12}{2 (2)} = 3$
$W = \sqrt{W_{0}^{2} - r^{2}} = \sqrt{5^{2} - 3^{2}} = 4 rad/sec$
$\frac{W - W_{0}}{W_{0}} \times 100 = \frac{4 - 5}{5} \times 100 = - \frac{1}{5} \times 100 = - 20 %$
Decreased by 20%

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