What is not part of the equation for angular momentum?

Scientists track _________________ to be able to predict geomagnetic storms and technological disturbances on Earth

Misha Larkins [42]

A. Sunspots and solar storms

6 0

3 years ago

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

What is the meaning of lightyear?

puteri [66]

"Lightyear" is a <em>distance</em> ... specifically, the distance that light travels
through vacuum in one year of 365 days.

It's equivalent to 9.454 x 10^12 kilometers, or 5.875 x 10^12 miles .

7 0

3 years ago

What happens when a substance undergoes a physical change?

vodka [1.7K]

A: Some physical properties change, but the substance keeps its identity.

8 0

3 years ago

Read 2 more answers

A carnot heat engine receives 600 kj of heat from a source of unknown temperature and rejects 175 kj of it to a sink at 20°c. de

oee [108]

(b) 71%

The thermal efficiency of a Carnot heat engine is given by:

$\eta = \frac{W}{Q_{in}}$

where

W is the useful work done by the engine

$Q_{in}$ is the heat in input to the machine

In this problem, we have:

$Q_{in}=600 kJ$ is the heat absorbed

$W=600 kJ-175 kJ=425 kJ$ is the work done (175 kJ is the heat released to the sink, therefore the work done is equal to the difference between the heat in input and the heat released)