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andrew11 [14]
2 years ago
7

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) fi

nd 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.
Physics
1 answer:
Zinaida [17]2 years ago
8 0

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

<h3 /><h3>What is amplitude?</h3>

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

#SPJ1

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K = 1/2 m v² = 15. 0 J

Solving for v², and replacing in the expression for T:

T = 1.9 Kg (3.97)² m²/s² / 0.042 m = 715 N

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wavelength.

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One complete expression of a waveform beginning at a certain point, progressing through the zero line to the wave’s highest (crest) and lowest (trough) points, and returning to the same value as the starting point is called a is called wavelength. Its can be also defined as the distance between two successive crests or trough points in wave form.

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The velocity of the crate vs time is given by the derivative of the position, so it is:

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Similarly, the acceleration of the crate vs time is given by the derivative of the velocity, so it is:

a(t)=v'(t)=\frac{d}{dt}(2.80+1.83t^2)=3.66t [m/s^2]

According to Newton's second law of motion, the force acting on the crate is equal to the product between mass and acceleration, so:

F(t)=ma(t)

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At t = 4.10 s, the acceleration of the crate is

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We have:

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If magnitudes is what is asked:

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<em>(N and </em>Kgm/s^2<em> are the same unit).</em>

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