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 0.206 kg is driven by a sinusoidal force at the oscillator's resonance frequency of 33.8 Hz. Find the value of the spring constant.

Answer 1

Answer:

Spring Constant K=9290.9550 N/m

Explanation:

Formula we are going to use is:

$2\pi f=\sqrt{\frac{K}{m}}$

Where:

f is the frequency

K is the spring constant

m is the mass

Given:

Mass of spring oscillator=m=0.206 kg

Resonance Frequency=f=33.8 Hz

Find:

Spring Constant=K=?

Solution:

From Above formula:

Taking Square on both sides

$4(\pi)^2f^2=\frac{K}{m} \\K=4(\pi)^2f^2*m\\K=4(\pi)^2(33.8)^2*(0.206)\\K=9290.9550 N/m$

Spring Constant K=9290.9550 N/m