Question

The light elastic rod supports a 4 kg sphere. when an 18n vertical force is applied to the sphere, the rod deflects 14 mm. a) find the amplitude and natural frequency of the system when the 18n force is suddenly released. b) if there is an earthquake and the wall oscillates with a harmonic frequency of 2 hz and an amplitude of 15 mm up and down, determine the amplitude of vibration for the sphere.

Answer 1

The amplitude of vibration for the sphere will be 29.48 nm.

What is amplitude?

The distance between from the crest of a wave to the next crest is known as the amplitude.

The amplitude of the sphere is;

$\rm A= \frac{\delta_0}{[1-(\frac{\omega}{\omega_n}^2]}$

The stiffness of the load is;

$\rm K = \frac{F}{\triangle y }\\\\ K=\frac{18}{0.014} \\\\ K=1285.71 \ N/m$

The natural frequency is;

$\rm \omega_n= \sqrt{\frac{k}{m}} \\\\ \rm \omega_n= \sqrt{\frac{1285.71}{4}} \\\\ \omega_n=17.93 \ rad/sec$

Put the obtained values in the amplitude formula;

$\rm A= \frac{0.015}{[1-(\frac{4 \pi}{17.93}^2]} \\\\ A= 0.02948 \\\\ A= 29.48 \ nm$

Hence,the amplitude of vibration for the sphere will be 29.48 nm.

To learn more about the amplitude, refer:

brainly.com/question/8662436

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