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stepan [7]
3 years ago
14

A spring-mass system has a spring constant of 3 N/m. A mass of 2 kg is attached to the spring, and the motion takes place in a v

iscous fluid that offers a resistance numerically equal to the magnitude of the instantaneous velocity. If the system is driven by an external force of (21 cos 3t − 14 sin 3t) N, determine the steady state response. Express your answer in the form R cos(ωt − δ). (Let u(t) be the displacement of the mass from its equilibrium position at time t.)

Physics
1 answer:
REY [17]3 years ago
7 0

Answer:

Ut = –(√2)/6 ×Cos(3t + π/4)

Explanation:

Please see the attachments below.

This problem requires some knowledge of calculus to solve as it deals with differential equations.

The solution has been explained in detail, step by step.

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A playground merry-go-round has a mass of 115 kg and a radius of 2.50 m and it is rotating with an angular velocity of 0.520 rev
tatuchka [14]

Answer:

W_f = 2.319 rad/s

Explanation:

For answer this we will use the law of the conservation of the angular momentum.

L_i = L_f

so:

I_mW_m = I_sW_f

where I_m is the moment of inertia of the merry-go-round, W_m is the initial angular velocity of the merry-go-round, I_s is the moment of inertia of the merry-go-round and the child together and W_f is the final angular velocity.

First, we will find the moment of inertia of the merry-go-round using:

I = \frac{1}{2}M_mR^2

I = \frac{1}{2}(115 kg)(2.5m)^2

I = 359.375 kg*m^2

Where M_m is the mass and R is the radio of the merry-go-round

Second, we will change the initial angular velocity to rad/s as:

W = 0.520*2\pi rad/s

W = 3.2672 rad/s

Third, we will find the moment of inertia of both after the collision:

I_s = \frac{1}{2}M_mR^2+mR^2

I_s = \frac{1}{2}(115kg)(2.5m)^2+(23.5kg)(2.5m)^2

I_s = 506.25kg*m^2

Finally we replace all the data:

(359.375)(3.2672) = (506.25)W_f

Solving for W_f:

W_f = 2.319 rad/s

7 0
3 years ago
An electron is released from rest in a uniform electric field and accelerates to the east at a rate of 4x106m/s2. What is the ma
Jet001 [13]

Answer:

Explanation:

Force on electron in an electric field E = eE where E is electric field .

acceleration = eE / m where m is mass of electron .

Putting the values

4 x 10⁶ = 1.6 x 10⁻¹⁹ x E / 9.1 x 10⁻³¹

E = 22.75 x 10⁻⁶ N/C

The direction of electric field will be towards west ( opposite to east )

because of negative charge on electron .

7 0
3 years ago
Which of the following statements best describes chromatic aberration?
Rzqust [24]

Answer:

The answer is A/B, they're the same answer anyways.

Explanation:

Chromatic aberration is the result when the lens fail to focus all the colors on the same point. The light then focuses in different points,and could lead to causing two images at once. The main culprit of this is usually dispersion.

6 0
3 years ago
Why would genetic material need to be able to reproduce
Lynna [10]
So that the next generation could inherit the previous adaptations and instinct and be similar to the parents. if that didn't happen, a cat might give birth to a giraffe
7 0
4 years ago
Một oto đang chuyển động thẳng đều với vận tốc 36km/h thì hãm phanh sau 20s thì ô tô dừng lại quãng đường oto đi được là
saw5 [17]
36km/h=10m/s
v=s/t=>s=200m
3 0
3 years ago
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