Running simulations in MATLAB - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of a simple simulation loop

What is the output of the following MATLAB code that simulates a simple process?

MATLAB

result = 0;
for i = 1:5
    result = result + i^2;
end
fprintf('%d\n', result);

A Error: Undefined variable 'result'

B 15

C 10

D 55

💡 Hint

Remember that i^2 means i squared and the loop adds these values.

The loop sums the squares of numbers from 1 to 5: 1+4+9+16+25 = 55.

🧠 Conceptual

intermediate

Understanding simulation time steps

In a simulation that updates a system every 0.1 seconds for 2 seconds, how many iterations will the simulation loop run?

A 20

B 2

C 10

D 200

💡 Hint

Divide total time by time step to find iterations.

2 seconds divided by 0.1 seconds per step equals 20 iterations.

🔧 Debug

advanced

Identify the error in this simulation code

What error will this MATLAB code produce when run?

MATLAB

time = 0:0.5:5;
for t = time
    y = sin(t);
end
fprintf('Final y: %f\n', y);

A No error, prints Final y: -0.958924

B Error: Index exceeds matrix dimensions.

C No error, prints Final y: 0.0

D Error: Undefined variable 'y'.

💡 Hint

Check the loop variable and how MATLAB handles for loops over arrays.

The loop iterates over each element in time, assigning y = sin(t). The final y is sin(5) ≈ -0.958924.

📝 Syntax

advanced

Syntax error in simulation update step

Which option contains the correct syntax to update the variable 'position' by adding velocity times time step 'dt' in MATLAB?

A position = position + velocity . dt;

B position = position + velocity * dt;

C position =+ velocity * dt;

D position += velocity * dt;

💡 Hint

MATLAB supports both explicit assignment and '+=' (R2016b+).

Option B uses correct MATLAB syntax in all versions. Option B uses '+=' which is valid since R2016b. Option B is a typo. Option B uses '.' incorrectly.

🚀 Application

expert

Result of a stochastic simulation

Consider this MATLAB code simulating a random walk for 3 steps starting at 0. What is the possible output of 'position' after running the code once?

MATLAB

position = 0;
steps = 3;
for i = 1:steps
    move = randi([-1 1]);
    position = position + move;
end
fprintf('%d\n', position);

A Only positive integers

B Only 0

C Any integer from -3 to 3

D Only negative integers

💡 Hint

Each step can move -1, 0, or +1, so position can vary widely.

Since each step can be -1, 0, or +1, after 3 steps position can be any integer between -3 and 3.

Practice

1. What is the main purpose of using a for loop in running simulations in MATLAB?

easy

A. To repeat a set of commands multiple times automatically

B. To create graphical user interfaces

C. To store data permanently on disk

D. To define new functions

Solution

1. Step 1: Understand the role of for loops

   A for loop repeats commands a fixed number of times, which is essential for running simulations step-by-step.

2. Step 2: Match the purpose to simulation needs

   Simulations require repeating calculations or processes many times to model changes over time, which for loops handle well.

3. Final Answer:

   To repeat a set of commands multiple times automatically -> Option A

4. Quick Check:

   Loop repeats commands = repeat steps [OK]

Hint: Loops repeat steps automatically, perfect for simulations [OK]

Common Mistakes:

• Confusing loops with data storage
• Thinking loops create GUIs
• Mixing loops with function definitions

2. Which of the following is the correct syntax to run a simulation loop 10 times in MATLAB?

easy

A. repeat 10 times
% simulation code
endrepeat

B. for i = 1:10
% simulation code
end

C. loop i = 1 to 10
% simulation code
endloop

D. while i < 10
% simulation code
end

Solution

1. Step 1: Recall MATLAB for loop syntax

   MATLAB uses for variable = start:end to run loops a fixed number of times.

2. Step 2: Compare options with correct syntax

   for i = 1:10 % simulation code end matches MATLAB syntax exactly; others use incorrect keywords or structures.

3. Final Answer:

   for i = 1:10 % simulation code end -> Option B

4. Quick Check:

   MATLAB loops use 'for i = start:end' [OK]

Hint: MATLAB loops use 'for i = start:end' syntax [OK]

Common Mistakes:

• Using non-MATLAB keywords like 'loop' or 'repeat'
• Confusing while with for loops
• Missing the end keyword

3. What will be the output of the following MATLAB code?

for t = 1:3
  disp(t^2)
end

medium

A. 1 4 9

B. 1 2 3

C. 2 4 6

D. Error: Undefined function

Solution

1. Step 1: Understand the loop iterations

   The loop runs with t = 1, 2, 3.

2. Step 2: Calculate the displayed values

   Each iteration displays t squared: 1^2=1, 2^2=4, 3^2=9.

3. Final Answer:

   1 4 9 -> Option A

4. Quick Check:

   Squares of 1,2,3 = 1 4 9 [OK]

Hint: Square each loop index to find output quickly [OK]

Common Mistakes:

• Printing t instead of t squared
• Confusing output with sums
• Expecting syntax errors

4. Identify the error in this MATLAB simulation code:

for i = 1:5
  result = i * 2
end
disp(result)

medium

A. Missing semicolon after result assignment

B. The loop variable 'i' is not initialized

C. No error; code runs and displays the last result

D. Variable 'result' is not defined before the loop

Solution

1. Step 1: Check variable initialization

   In MATLAB, variables can be created inside loops without prior definition.

2. Step 2: Understand loop and output behavior

   The loop runs 5 times, updating 'result' each time; after loop, 'result' holds last value (5*2=10), which is displayed.

3. Final Answer:

   No error; code runs and displays the last result -> Option C

4. Quick Check:

   Loop updates variable; last value shown [OK]

Hint: Variables inside loops update each iteration; last value remains [OK]

Common Mistakes:

• Thinking semicolons are mandatory to avoid errors
• Assuming variables must be pre-declared
• Confusing loop variable initialization

5. You want to simulate the growth of a population starting at 100, increasing by 10% each step, for 5 steps. Which MATLAB code correctly runs this simulation and stores all population values in an array pop?

hard

A. pop = zeros(5,1);
pop(1) = 100;
for i = 1:5
pop(i+1) = pop(i) * 1.1;
end

B. pop = 100;
for i = 1:5
pop = pop * 1.1;
end

C. pop = [];
for i = 1:5
pop(i) = 100 * 1.1^i;
end

D. pop = zeros(1,5);
pop(1) = 100;
for i = 2:5
pop(i) = pop(i-1) * 1.1;
end

Solution

1. Step 1: Understand the simulation requirements

   Start at 100, increase by 10% each step, store all 5 values in an array.

2. Step 2: Analyze each option for correctness

   pop = zeros(1,5); pop(1) = 100; for i = 2:5 pop(i) = pop(i-1) * 1.1; end initializes array, sets first value, then correctly updates subsequent values using previous step's value. pop = 100; for i = 1:5 pop = pop * 1.1; end overwrites single value, no array. pop = []; for i = 1:5 pop(i) = 100 * 1.1^i; end calculates powers but starts from step 1, missing initial 100 at index 1. pop = zeros(5,1); pop(1) = 100; for i = 1:5 pop(i+1) = pop(i) * 1.1; end tries to access index 6 in 5-element array, causing error.

3. Final Answer:

   pop = zeros(1,5); pop(1) = 100; for i = 2:5 pop(i) = pop(i-1) * 1.1; end -> Option D

4. Quick Check:

   Initialize array, set first value, update from previous [OK]

Hint: Initialize array, set first value, update from previous step [OK]

Common Mistakes:

• Not storing all values in an array
• Indexing beyond array size
• Overwriting single variable instead of array