Question

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?

Answer 1

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