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A 1 newton force will stretch a spring 1 meter. The spring/mass system is damped by a force that is 8 times the instantaneous ve

sukhopar [10]

Answer:

Step-by-step explanation:

Given the mass is m =16kg, and 1N force will stretch the spring 1 m.

That is, F =1N,Z =1m. Now find the spring constant k:

F = kL = 1 = k(1) = k= 1N/m.

The damping force is 8times the instantaneous velocity, this means β = 8,

and the external force is f(t) = 0

Initially the object compressed 0.6m above equilibrium position,

with the downward velocity is 2m/s.

The differential equation for a spring mass system with

damping force and extemal force is: mx" + βxt + kx = f(t).

so, 16x"+ 8x' + x= 0, x(0} = -0.6, x'(0)= 2m/s.

Now solve the DE:

The auxilary equation for the homogeneous equation is 16x"+8x'+x=0

solving we get, 16r² + 8r + 1 = 0 => (4r + 1)² = 0 => r = - 1/4.

Then the general solution for the homogenous system is: $x(t)=c_1e^{-t/4} +c_2te^{-t\4}$ .

Use the initial conditions x (0) = -0.6, x'(0) = 2m/s:

$x(0)=c_1e^{0} +c_2(0)e^{0}=-0.6=c_1\\x'(t)=-\frac{1}{4}c_1e^{-t/4}+c_2e^{-t/4}-\frac{1}{4}c_2te^{-t/4}\\x'(0)=-\frac{1}{4}c_1e^0+c_2e^0-\frac{1}{4}c_2(0)e^0=2=-\frac{1}{4}(-0.6)+c_2=c_2=1.85$ .

Hence, $x(t) =-0.6e^{-t/4}+1.85te^{-t/4}$ .

5 0

3 years ago

Pls help due today or ill fail

Nezavi [6.7K]

Answer: Ok so I may be wrong but I got 84ft

Step-by-step explanation: The bottom looks like a rectangle so it would be 4 times 12. 4 times 12 equals 48. since the height is 4 it would be 10-4 which equals 6. 6 Times 12 divided by two equals 36. 36 plus 48 is 84.

7 0

3 years ago

A ski resort claims that there is a 75% chance of snow on any given day in january and that snowfall happens independently from

lys-0071 [83]

Using the binomial distribution, it is found that the mean and the standard deviation of variable x are given as follows:

$\mu = 3, \sigma = 0.87$

<h3>What is the binomial probability distribution?</h3>

It is the probability of exactly <u>x successes on n repeated trials, with p probability</u> of a success on each trial.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

In this problem, we have that the parameters are given as follows:

n = 4, p = 0.75.

Hence the mean and the standard deviation are given as follows:

E(X) = np = 4 x 0.75 = 3.

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{4 \times 0.75 \times 0.25} = 0.87$

More can be learned about the binomial distribution at brainly.com/question/24863377

#SPJ1

7 0

2 years ago

Please help. It’s due today

vladimir1956 [14]

Answer:

There's nothing there I believe you forgot to add a link just add or create another question and i'll see what I can do :)

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Please help and explain how you solved it. Thanks.

galina1969 [7]

Answer:

This is 0.14 to the nearest hundredth

Step-by-step explanation:

Firstly we list the parameters;

Drive to school = 40

Take the bus = 50

Walk = 10

Sophomore = 30

Junior = 35

Senior = 35

Total number of students in sample is 100

Let W be the event that a student walked to school

So P(w) = 10/100 = 0.1

Let S be the event that a student is a senior

P(S) = 35/100 = 0.35

The probability we want to calculate can be said to be;

Probability that a student walked to school given that he is a senior

This can be represented and calculated as follows;

P( w| s) = P( w n s) / P(s)

w n s is the probability that a student walked to school and he is a senior

We need to know the number of seniors who walked to school

From the table, this is 5/100 = 0.05

So the Conditional probability is as follows;

P(W | S ) = 0.05/0.35 = 0.1429

To the nearest hundredth, that is 0.14

3 0

3 years ago