Help please, will give brainlist!

Write the differential equation that governs the motion of the damped mass-spring system, and find the solution that satisfies t

melisa1 [442]

This question is incomplete, the complete question is;

Write the differential equation that governs the motion of the damped mass-spring system, and find the solution that satisfies the initial conditions specified. Units are mks; γ is the damping coefficient, with units of kg/sec

m = 0.2, γ = 1.6 and k = 4

Initial displacement is 1 and initial velocity is -2

x" + _____ x' ____x = 0

x(t) =

Answer:

the solution that satisfies the initial conditions specified is;

x(t) = $c_1e^{-4t}cos(2t)$ + $c_2e^{-4t}sin(2t)$

Explanation:

Given the data in the question ;

m = 0.2, γ = 1.6, k = 4

x(0) = 1, x'(0) = -2

Now, the differential equation that governs the motions of spring mass system is;

mx" + γx' + kx = 0

so we substitute

0.2x" + 1.6x' + 4x = 0

divide through by 0.2

x" + 8x' + 20x = 0

hence, characteristics equation will be;

m² + 8m + 20 = 0

we find m using; x = [ -b±√(b² - 4ac) ] / 2a

m = [ -8 ± √((8)² - 4(1 × 20 )) ] / 2(1)

m = [ -8 ± √( 64 - 80 ) ] / 2

m = [ -8 ± √-16 ) ] / 2

m = ( -8 ± 4i ) / 2

m = -4 ± 2i

Hence, the general solution of the differential equation is;

x(t) = $c_1e^{-4t}cos(2t)$ + $c_2e^{-4t}sin(2t)$

From the initial conditions;

c₁ = 1, c₂ = 1

the solution that satisfies the initial conditions specified is;

x(t) = $c_1e^{-4t}cos(2t)$ + $c_2e^{-4t}sin(2t)$

6 0

3 years ago

Which of the following statements regarding heuristics and empiricism is true? A. Heuristics allows a priori theoretical concep

WITCHER [35]

Answer: <em>Option (A) is correct.</em>

Explanation:

A heuristic is often referred to as an approach to solving problems or discovery that subjects a method, which is considered to be practical although might not be guaranteed to be perfect, optimal, or rational, but sufficient for reaching to goal.

Empiricism is known as a theory under which one can states that knowledge can only be imparted from the sensory experience. It is considered to be one of the main notions underlying in epistemology, i.e. known as the study of human knowledge, alongside skepticism and rationalism.

5 0

3 years ago

What is the mass of a 5000 N car on Earth?

puteri [66]

Answer:

510.2kg

Explanation:

use w=mg then put the value you will get answer

4 0

3 years ago

A 50.0 kg object is moving at 18.2 m/s when a 200 N force is applied opposite the direction of the objects motion, causing it to

Gekata [30.6K]

Answer:

t = 1.4[s]

Explanation:

To solve this problem we must use the principle of conservation of linear momentum, which tells us that momentum is conserved before and after applying a force to a body. We must remember that the impulse can be calculated by means of the following equation.

$P=m*v\\or\\P=F*t$

where:

P = impulse or lineal momentum [kg*m/s]

m = mass = 50 [kg]

v = velocity [m/s]

F = force = 200[N]

t = time = [s]

Now we must be clear that the final linear momentum must be equal to the original linear momentum plus the applied momentum. In this way we can deduce the following equation.

$(m_{1}*v_{1})-F*t=(m_{1}*v_{2})$

where:

m₁ = mass of the object = 50 [kg]

v₁ = velocity of the object before the impulse = 18.2 [m/s]

v₂ = velocity of the object after the impulse = 12.6 [m/s]

$(50*18.2)-200*t=50*12.6\\910-200*t=630\\200*t=910-630\\200*t=280\\t=1.4[s]$

3 0

3 years ago

What best describes myotibrils

krok68 [10]

Myofibrils are composed of long proteins such as actin, myosin, and titin, and other proteins that hold them together. These proteins are organized into thin filaments and thick filaments, which repeat along the length of the myofibril in sections called sarcomeres. Muscles contract by sliding the thin (actin) and thick (myosin) filaments along each other.

8 0

3 years ago