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Tcecarenko [31]
3 years ago
14

A mass weighting 16 lbs stretches a spring 3 inches. The mass is in a medium that exerts a viscous resistance of 20 lbs when the

mass has a velocity of 4 ft/sec. Suppose the object is displaced an additional 7 inches and released. Find an equation for the object's displacement, u(t), in feet after t seconds.
Physics
1 answer:
const2013 [10]3 years ago
3 0

Answer:

The equation for the object's displacement is u(t)=0.583cos11.35t

Explanation:

Given:

m = 16 lb

δ = 3 in

The stiffness is:

k=\frac{m}{\delta } =\frac{16}{3} =5.33lb/in

The angular speed is:

w=\sqrt{\frac{k}{m} } =\sqrt{\frac{5.33*386.4}{16} } =11.35rad/s

The damping force is:

F_{D} =cu

Where

FD = 20 lb

u = 4 ft/s = 48 in/s

Replacing:

c=\frac{F_{D} }{u} =\frac{20}{48} =0.42lbs/in

The critical damping is equal:

c_{c} =\frac{2k}{w} =\frac{2*5.33}{11.35} =0.94lbs/in

Like cc>c the system is undamped

The equilibrium expression is:

u(t)=u(o)coswt+u'(o)sinwt\\u(o)=7=0.583\\u'(o)=0\\u(t)=0.583coswt\\u(t)=0.583cos11.35t

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Feliz [49]

Answer:

32 cm

Explanation:

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Since the lens produce the image with same size as object, magnification is given as

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q = distance of the image from the lens

magnification is given as

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Using the lens equation, we get

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using eq-1

1/p + 1/p = 1/16

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Answer:

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We know by the question that:

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Finally we change the angular velocity from rad/s to rpm as:

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The sun’s___and the planet’s___keeps planets moving is___orbits.
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Explanation:

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2) The inertia of the planet. In fact, according to Newton's first law, an object in motion at constant velocity will continue moving at its velocity, unless acted upon an external unbalanced force. Therefore, the planet tends to continue its motion in a straight line (tangential to the circular orbit), however it turns in a circle due to the presence of the gravitational attraction of the Sun.

Learn more about gravity:

brainly.com/question/1724648

brainly.com/question/12785992

#LearnwithBrainly

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