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The curvilinear motion of a particle is defined by the following parametric equations
𝑥 = 52𝑡 − 9𝑡
2
, 𝑦 = 125 − 5𝑡
3
The velocity of a particle is defined by 𝑣 = √𝑣𝑥
2 + 𝑣𝑦
2. For time interval [0 6] make a first
plot that shows the position of the particle ( y vs x) and a second plot ( on the same figure
window) of the velocity of the particle as a function of time. In addition, using an asterisk
marker show the position of the particle ( in first plot ) at which its speed is maximum. For time
use a vector with spacing of 0.1s.
Write a MATLAB code to solve the following difference equations by z-transform and display the solutions by stem plots:
2) Suppose that the number of bacteria in a colony doubles every hour. If a colony begins with five bacteria, how many will be present in n hours?
Write a MATLAB code to solve the following difference equations by z-transform and display the solutions by stem plots:
3) A bank account gives an interest rate of 5% compounded monthly. If you invest initially Rs .1000 and add Rs. 10 every month. How much money do you have after 5 years?
Write a MATLAB code to solve the following difference equations by z-transform and display the solutions by stem plots:
2) Suppose that the number of bacteria in a colony doubles every hour. If a colony begins with five bacteria, how many will be present in n hours?
Write a MATLAB code to solve the following difference equations by z-transform and display the solutions by stem plots:
1) An amount of USD 10,000 $ is deposited in a bank account with an annual interest
rate of 4%. Determine the balance of the account after 15 years.
Write a MATLAB code to solve the following difference equations by z-transform and display the solutions by stem plots:
1) An amount of USD 10,000 $ is deposited in a bank account with an annual interest
rate of 4%. Determine the balance of the account after 15 years.
2) Suppose that the number of bacteria in a colony doubles every hour. If a colony begins with five bacteria, how many will be present in n hours?
3) A bank account gives an interest rate of 5% compounded monthly. If you invest initially Rs .1000 and add Rs. 10 every month. How much money do you have after 5 years?
Create a row vector which contains the sum of each column in a matrix of unknown dimensions – use the matrix shown below as your test data: [2 -5 6 7; -4 8 -5 6] Display the resulting row vector as follows: The sum of column 1 is -2.00 … The sum of column 4 is 13.00
Write a function to calculate the gravitational force F between two bodies given their masses (m1 and m2) and the distance r between them as given above.
Write a script Gravity to test your function by determining the gravitational force (force) of an 800kg satellite (m2) in orbit 38 000km (r – note that r should be in metres) above the Earth. The mass (m1) of the Earth is 5.98 × 1024kg.
You need to take a matrix of any size, doubles all the elements that are positive and add 10 to all
the elements that are zero or negative. Then you need to add all the elements of the array and
display the results as follows, with the total value displayed to 3 decimal places:
The sum of the matrix elements is 75.322
i. Write a function called matrixfx
Use the input matrix xin[n,m] sent by the script,
Initialise your out variable xout [n,m]
to perform the above calculations on the positive and negative numbers, depending on
the values of each element of the matrix – Tip use one logical array mask to build the
matrix xout [n,m]. No loops!
ii. Write a script called matrixAdd
Use the function matrixfx to manipulate the test data as indicated above (y).
Initialise the necessary variables to use nested loops to add up the elements of the matrix
y.
Your display should be formatted to display the final total as indicated above.
How to express a 3rd order differential equation into three first order differential equations?
Explain.
