### Trajectory Calculation and Averaging Coordinates#### Step 2: Calculating the TrajectoryThe code calculates the trajectory \( \mathbf{r}(t) \) and stores the coordinates for time steps \( \Delta t \) as a nested list `trajectory`, which contains:\[ [ [x_0, y_0, z_0], [x_1, y_1, z_1], [x_2, y_2, z_2], \ldots ] \]- Start from time \( t = 0 \) and use a time step \( \Delta t = 0.01 \).- The last data point in the trajectory should be the time when the oscillator "hits the ground", i.e., when \( z(t) \leq 0 \).#### Step 3: Time and Position at Ground ContactThe code calculates the time for hitting the ground (i.e., the first time \( t \) when \( z(t) \leq 0 \)) and stores it in the variable `t_contact`. The corresponding positions are stored in the variables `x_contact`, `y_contact`, and `z_contact`. **Example Output:**```plaintextt_contact = 1.430x_contact = 0.755y_contact = -0.380z_contact = ...```*(The partial example output is for \( z_0 = 10 \). Floating point numbers are outputted with 3 decimals using `format()`, e.g., `t_contact = {:.3f}.format(t_contact)`.)*#### Step 4: Calculating the Average CoordinatesThe code calculates the average x- and y-coordinates using the formulas:\[ \overline{x} = \frac{1}{N} \sum_{i=1}^{N} x_i \]\[ \overline{y} = \frac{1}{N} \sum_{i=1}^{N} y_i \]where \( x_i, y_i \) are the coordinates \( x(t), y(t) \) in the trajectory, and \( N \) is the number of data points that you calculated.Store the result as a list in the variable `center`:\[ \text{center} = [\overline{x}, \overline{y}] \]**Example Output:**```plaintextcenter = [0.917, .... **Study of Dropped 2D Harmonic Oscillator****Introduction:**A mass \( m \) is held by two perpendicular identical springs in space in the \( x\)-\(y \) plane and is dropped from a height \( z_0 \) under the influence of gravity. Let's call this setup the "dropped 2D harmonic oscillator." The mass moves in a potential described by:\[ U(x, y, z) = \frac{1}{2}k(x^2 + y^2) + mgz \]The motion ends when the mass hits the ground at \( z = 0 \). The exact expression for \( U(x, y, z) \) is given for context but is not necessary for solving the problem directly.**Trajectory of the Mass:**The mass follows a trajectory, which is its curve in space, \( \mathbf{r}(t) = (x(t), y(t), z(t)) \), given by:\[\begin{align*}x(t) &= A \cos(\omega t) \\y(t) &= B \cos(\omega t + \phi) \\z(t) &= -\frac{1}{2}gt^2 + z_0\end{align*}\]where the amplitudes \( A \), \( B \), and the phase difference \( \phi \) are determined by the initial conditions, and the frequency \( \omega \) is:\[ \omega = \sqrt{\frac{k}{m}} \]**Given Conditions:**- \( A = 1 \)- \( B = 2 \)- \( \phi = \pi/3 \)- \( \omega = 0.5 \)- \( g = 9.81 \)**Task:**Develop a program that:1. Reads the initial drop height \( z_0 \) from user input.

Solution in the image given below

gravity (let's call this the "dropped 2D harmonic oscillator"). The mass moves in a potential U (x, y, z) = k(x² + +mgz and the motion stops when the mass hits the ground at z = 0. (You don't need U(x, y, z) for solving the problem and it is only provided for the exact physics context.) The trajectory of the mass, i.e, its curve in space, r(t) = (x(t), y(t), z(t)) is x(t) = A cos(wt) y(t) = B cos(wt + p) 1 z(t) = - =gt² + 20 are determined by the initial conditions, and the frequency is w = √k/m. where the amplitudes A, B and the phase difference Given A = 1, B = 2,0 = π/3, w = 0.5, and g = 9.81, write a program that

gravity (let's call this the "dropped 2D harmonic oscillator"). The mass moves in a potential U (x, y, z) = k(x² + +mgz and the motion stops when the mass hits the ground at z = 0. (You don't need U(x, y, z) for solving the problem and it is only provided for the exact physics context.) The trajectory of the mass, i.e, its curve in space, r(t) = (x(t), y(t), z(t)) is x(t) = A cos(wt) y(t) = B cos(wt + p) 1 z(t) = - =gt² + 20 are determined by the initial conditions, and the frequency is w = √k/m. where the amplitudes A, B and the phase difference Given A = 1, B = 2,0 = π/3, w = 0.5, and g = 9.81, write a program that

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

See similar textbooks

Similar questions

Reimplement the digital clock from the preceding exercise, representing the time as the minutes from midnight. This makes the pulse member function very easy, but you have to work harder to recover the hours and minutes. For example, 100 minutes after midnight is 1 hour and 40 minutes.
Lets say we are creating a python game. A word is displayed gets displayed on the screen. The players of the game must type as many words as they an that are related to the word that is displayed. If players type in the same word multiple times, it is ignored. One the players are done taking turns, the program gives each player a score that is based off how many wrods they entered that are similiar to what other words players have entered. So for a player to get a point, the word they typed must be typed by another student. QUESTION: We need to store the words typed by the players and all words etered. Would we use a list, set, dict or tuple?
Computer Science Write a Java program that reads a line and a line segment and then determines whether they intersect or not. When they overlap completely, consider that as intersecting. Use variables ((lp1x, lp1y), (lp2x, lp2y)) to represent a line and ((sp1x, sp1y), (sp2x, sp2y)) to represent a line segment
in Java
Implement the problem below in Python using mpi4py. Submit the code of your program and a brief report. The report should describe the design of your program, and demonstrate the results of running your program. n-body solver. Implement a parallel n-body solver with n = 10 particles. You may randomly generate the masses, initial velocities, and initial positions of all particles at the beginning. Compute the positions of all particles after 1 second. Compare the results by using 0.1s, 0.01s, and 0.001s as the time in each timestep, respectively.
Using Python, Triangle A has vertices at (−1,0), (1, 0), and (0, 1). Triangle B has vertices at (0, 0), (0, 6), and (3, 3) on a standard x - y coordinate system with +x pointing to the right and +y pointing up. 1. Use the cross product to calculate the area of each triangle.
Consider two traffic lights in a junction that each one has a 7-segment display to show the remaining time. The traffic lights are working as follows: State1: Traffic light 1=GREEN Traffic light 2=RED for 10 seconds,State2: Traffic light 1=YELLOW Traffic light 2=YELLOW for 2 seconds,State3: Traffic light 1=RED Traffic light 2=GREEN for 6 seconds,GOTO State1 During each step, the amount of remaining time should be displayed on the 7-segment and it should be updated every one second. For example in State 1, the display shows 9, then after a second it shows 8, and ... finally, it shows 0 for one second, and the control moves to State 2Write an 8051 assembly program according to the Edsim51 configuration, LED 0, LED1 and LED 2 construct the first traffic light, and LED 3, LED 4, and LED 5 can be used for the 2nd traffic light. Assume that the lookup table for 7segment exists on memory at address 0F00h