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jek_recluse [69]

2 years ago

9

The position of an object that is oscillating on a spring is given by the equation x = (17.4 cm) cos[(5.46 s-1)t]. what is the a

ngular frequency for this motion?

1 answer:

bulgar [2K]2 years ago

6 0

The angular frequency of this motion is 5.46 rad/s.

The oscillation of spring is an example of Simple Harmonic Motion(SHM).

The general equation of an SHM is given by the formula.

X = Acos(wt)

Here A is the amplitude

ω is the angular frequency

T is the time

Comparing the above equation with the given condition,

X = 17.4 cm cos(5.46t)

A = 17.4 cm

ω = 5.46 rad/s

T = 1 s

Hence, the angular frequency of this motion is 5.46 rad/s.

To know more about the "general equation of SHM", refer to the link below:

brainly.com/question/14869852?referrer=searchResults

#SPJ4

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pshichka [43]

Answer:

a) $\theta = 52\,rad$ , b) $v_{A} = 44\cdot r \,\frac{m}{s}$ , c) $a_{A,n} = 1936\cdot r\,\frac{m}{s^{2}}$ , $a_{A,t} = 24\cdot r\,\frac{m}{s^{2}}$

Explanation:

a) The angular motion is obtained by integrating the angular acceleration function twice:

$\alpha = 3\cdot t^{2} + 12$

$\omega = t^{3} + 12\cdot t + 12$

$\theta = \frac{1}{4}\cdot t^{4} + 6\cdot t^{2} + 12\cdot t$

The angular motion when t = 2 s. is:

$\theta = \frac{1}{4}\cdot (2\,s)^{4} + 6\cdot (2\,s)^{2} + 12\cdot (2\,s)$

$\theta = 52\,rad$

b) Let be $r$ the distance between A and the rotation axis, measured in meters. The magnitude of the angular velocity when t = 2 s. is:

$\omega = (2\,s)^{3} + 12\cdot (2\,s) + 12$

$\omega = 44\,\frac{rad}{s}$

Finally, the magnitude of the velocity is:

$v_{A} = 44\cdot r \,\frac{m}{s}$

c) The angular acceleration of the disk when t = 2 s. is:

$\alpha = 3\cdot (2\,s)^{2} + 12$

$\alpha = 24\,\frac{rad}{s^{2}}$

Lastly, the normal and tangential components at point A are, respectively:

$a_{A,n} = \omega^{2}\cdot r$

$a_{A,n} = \left(44\right)^{2}\cdot r$

$a_{A,n} = 1936\cdot r\,\frac{m}{s^{2}}$

$a_{A,t} = \alpha \cdot r$

$a_{A,t} = 24\cdot r\,\frac{m}{s^{2}}$

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3 years ago

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alexgriva [62]

Answer:

$\phi=4.52 rad$

Explanation:

From the question we are told that

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3 years ago