P 1-2 (5 Marks)
The Arrhenius equation is widely used to describe plenty of physical phenomena. Based on the
equation and conditions shown below, write a script that can generate the figure of as a
function of .
Figure 2. Conditions and the equation of P 1-2
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Problem 2 Matrix Operation (15 Marks)
P 2-1 (5 Marks, 1 Mark for each small question)
Type this matrix in MATLAB and use MATLAB to carry out the following instructions.
a) Create a vector consisting of the elements in the third column of .
b) Create a vector consisting of the elements in the second row of .
c) Create a 4 x 3 array consisting of all elements in the second through fourth columns of
.
d) Create a 3 x 4 array consisting of all elements in the second through fourth rows of .
e) Create a 2 x 3 array consisting of all elements in the first two rows and the last three
columns of .
P 2-2 (5 Marks, 1 Mark for each small question)
Consider the following arrays:
Write MATLAB expressions to do the following.
a) Select just the third row of B.
b) Evaluate the sum of the second row of B.
c) Multiply the second column of B and the first column of A element by element.
d) Evaluate the maximum value in the vector resulting from element-by-element multiplication
of the second column of B with the first column of A.
e) Use element-by-element division to divide the first row of A by the first three elements of
the third column of B. Evaluate the sum of the elements of the resulting vector.
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P 2-3 (5 Marks)
The figure shows the forces in the eight-member truss. The forces can be determined by solving
a system of linear equations using the sets of equations shown below. Using the equations
shown below, set the system of linear equations and get the solutions of the forces.
Problem 3 (30 Marks)
P 3-1 (15 Marks, 10 Marks for programming and 5 Marks for displaying results)
The equation of motion for a pendulum whose base is accelerating horizontally with an
acceleration a(t) is
the following three cases:
a) The acceleration is constant:.
b) The acceleration is constant:
c) The acceleration is linear with time: .
Figure 3. Forces in the eightmember truss for P 2-3.
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P 3-2 (15 Marks, 10 Marks for programming and 5 Marks for displaying results)
The following equation describes the motion of a certain mass connected to a spring, with no
friction
Problem 4 (25 Marks, with 1) 15 Marks, 2) 10 Marks)
Consider a circuit system as shown in Figure 4.
Figure 4. A circuit with multiple resistors and inductors for Problem 4.
Question:
Problem 5 (20 Marks, with 1) 5 Mark, 2) 5 Marks, 3) 10 Marks)
1) In Simulink, generate a model that simulates 5sin(2pi * 60t) with time between 0 and 0.2
seconds and show the result using the scope of Simulink.
2) In Simulink, generate a model that simulates 2sin(50t) with time between 0 and 5 seconds
and show the result using the scope of Simulink.
3) Using Simulink, generate a model that can solve 1
2
̈+ 2
5
̇ + = with the initial
conditions of (0) = 1 ̇(0) = 2. Set the simulation time between 0 to 10 seconds and show
the result using the scope of Simulink.
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