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skad [1K]
2 years ago
11

What is the least common multiple of 5 and 8?​

Mathematics
1 answer:
denis-greek [22]2 years ago
5 0
40

(Mark me the brainliest)
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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
2 years ago
One number is 4 times number another. Their sum is 35. Find the number
jonny [76]

Answer:

7

Step-by-step explanation:

n+4n=35

5n=35

5n/5=35/5

n=7

3 0
3 years ago
What is the remainder when 4x^3+2x^2-18+38/x-3
Trava [24]

Answer:

The remainder is 2

Step-by-step explanation:

Hope this helps uwu

7 0
3 years ago
Angle A is an acute angle in a right triangle
Brrunno [24]
Cos= 24/25

7^2+24^2=25^2
3 0
3 years ago
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There are 320 rods in a mile Find the length of a rod in feet
faust18 [17]
The answer should be 320 rods = 1 mile 5280 ft= 1 mile
Hope this helps you

3 0
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