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?

Question

Physics

Brenden

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)

Know the Answer?

Charlize Hill · 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