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22 December, 18:20

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?

+5
Answers (1)
  1. 22 December, 19:34
    0
    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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