The James Webb Space Telescope (JWST) is a new space telescope currently under construction. The JWST will orbit the Sun in an orbit roughly 1.5 million km from the earth, in a position with the Earth between the telescope and the Sun. The primary mirror of the JWST will consist of 18 hexagonally shaped segments that when fitted together will be 6.5 min diameter (over 2.5 times the diameter of the Hubble). With a larger mirror, the JWST will be able to collect more light to “see" deeper into space. The primary mirror when pieced together will function as a parabolic mirror with a focal length of 131.4 m . Suppose that a coordinate system is chosen with 0 , 0 at the center of a cross section of the primary mirror. Write an equation of the parabolic cross section of the mirror for − 3.25 ≤ x ≤ 3.25 . Assume that x and y are measured in meters.
The James Webb Space Telescope (JWST) is a new space telescope currently under construction. The JWST will orbit the Sun in an orbit roughly 1.5 million km from the earth, in a position with the Earth between the telescope and the Sun. The primary mirror of the JWST will consist of 18 hexagonally shaped segments that when fitted together will be 6.5 min diameter (over 2.5 times the diameter of the Hubble). With a larger mirror, the JWST will be able to collect more light to “see" deeper into space. The primary mirror when pieced together will function as a parabolic mirror with a focal length of 131.4 m . Suppose that a coordinate system is chosen with 0 , 0 at the center of a cross section of the primary mirror. Write an equation of the parabolic cross section of the mirror for − 3.25 ≤ x ≤ 3.25 . Assume that x and y are measured in meters.
The James Webb Space Telescope (JWST) is a new space telescope currently under construction. The JWST will orbit the Sun in an orbit roughly
1.5
million km from the earth, in a position with the Earth between the telescope and the Sun. The primary mirror of the JWST will consist of
18
hexagonally shaped segments that when fitted together will be
6.5
min diameter (over
2.5
times the diameter of the Hubble). With a larger mirror, the JWST will be able to collect more light to “see" deeper into space.
The primary mirror when pieced together will function as a parabolic mirror with a focal length of
131.4
m
. Suppose that a coordinate system is chosen with
0
,
0
at the center of a cross section of the primary mirror. Write an equation of the parabolic cross section of the mirror for
−
3.25
≤
x
≤
3.25
. Assume that x and y are measured in meters.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
2. Consider the following:
Prove that x, x2, and 1/x are the solutions to the homogeneous equation
corresponding to x³y"" + x²y" + 2xy' + 2y = 2x4.
b. use variation of parameters to find a particular solution and complete the general
solution to the differential equation. I am interested in process. You may use a
computer for integration, finding determinants and doing Kramer's.
3. A spring is stretched 6 in. by a mass that weighs 8 lb. The mass is attached to a dashpot
mechanism that has a damping constant of 0.25 lb-sec./ft. and is acted on by an external
force of 4 cos 2t lb.
a. Set-up the differential equation and initial value problem for the system.
b. Write the function in phase-amplitude form.
C.
Determine the transient solution to the system. Show your work.
d. Determine the steady state of this system. Show your work.
e.
Is the system underdamped, overdamped or critically damped? Explain what this
means for the system.
4. Suppose that you have a circuit with a resistance of 20, inductance of 14 H and a
capacitance of 11 F. An EMF with equation of E(t) = 6 cos 4t supplies a continuous charge
60
to the circuit. Suppose that the q(0)= 8 V and the q'(0)=7. Use this information to answer the
following questions
a. Find the function that models the charge of this circuit.
b. Is the circuit underdamped, overdamped or critically damped?
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY