Engineers can determine properties of a structure that is modeled as a damped spring oscillator, such as a bridge, by applying a driving force to it. a weakly damped spring oscillator of mass
0.246
kg is driven by a sinusoidal force at the oscillator's resonance frequency of
27.8
hz. find the value of the spring constant.
the amplitude of the driving force is
0.543
n and the amplitude of the oscillator's steady‑state motion in response to this driving force is
0.877
m. what is the oscillator's damping constant?

The value of spring constant and the oscillator's damping constant is

K= 6605.667008, b= 0.002884387

Explanation:

For Weakly damping spring oscillator

K/m = W_0^2     (at resonance)

K= mW_0^2

=0.206 * ( 2π * 28.5) ^2

=0.206 * (2π)^2 * (28.5)^2

K= 6605.667008

F = - bV

b= -F/V = -F/ -W_0 * m

=F/W_0 * m

= 0.438N / 2π * 28.5 * 0.848

b= 0.002884387

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