Muhammad AdnanEngineering & designIdeas engineered. Solutions delivered.

Simulation & Control

Report-based engineering study

MATLAB Signals & Vibration Response

MATLAB modeling and visualization spanning a spring–mass–damper sensor, sampled sinusoids and complex exponential signals.

MATLABControl System Toolbox functionstfstepimpulse
Two MATLAB time-response charts over a 0.01-second interval. Enlarge image
Original step and impulse plots for the documented vibration-model parameter case.
Four discrete sinusoid stem plots labeled with different multiples of pi over eight. Enlarge image
Stacked sample plots compare four of the report’s sinusoidal frequency settings.
Real and imaginary damped oscillations above a decaying magnitude trace and wrapped phase trace. Enlarge image
Original damped complex-signal plots; the lower panel displays the magnitude and phase traces produced by the code.
MATLAB code sets mass, stiffness and damping and calls step and impulse. Enlarge image
Original MATLAB definition of the parameterized transfer function and transient plotting calls.
MATLAB Signals & Vibration Response — architecture diagram Enlarge image
Explanatory architecture for this project; source software evidence is shown separately.

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Project brief

This project brings together mathematical system modeling and several MATLAB signal-visualization exercises. It begins with a spring–mass–damper representation of a vibration sensor and introduces relative displacement between the moving mass and its base. The report develops the governing equation and a transfer-function form, then supplies MATLAB code using tf, step and impulse to examine a specified parameter case over a 0.01-second interval. The documented parameters include a mass of 4.8 × 10⁻⁵ kg and spring stiffness of 800 N/m. Later exercises broaden the work to discrete-time impulses, delayed sequences, unit steps and sampled sinusoids. A set of stacked plots compares sinusoidal sequences for several angular-frequency choices, making the change in sample pattern visible. Continuous-time complex exponential examples then separate real, imaginary, magnitude and phase components; the damped example uses an exponentially decaying envelope. The project’s useful evidence is its progression from mathematical expressions to executable MATLAB statements and labeled plots. The selected gallery preserves that progression with the transfer-function code, transient response plots, sampled-sinusoid comparisons and complex-signal output. Some frequency-analysis calculations and interpretations in the source are inconsistent, so this brief does not claim a verified sensor bandwidth or optimal damping choice. It presents the supported modeling and plotting workflow without extending the report into experimental sensor validation.

The engineering challenge

Translate mechanical and signal equations into MATLAB representations while keeping continuous-system response plots and discrete-time sequence examples understandable.

Engineering approach

  1. Represent relative motion in a spring–mass–damper sensor and formulate the transfer function.
  2. Define the stated parameter case in MATLAB and plot step and impulse responses.
  3. Generate discrete impulses, step sequences and sampled sinusoidal signals with explicit time indices.
  4. Compare sinusoidal sample patterns across multiple angular-frequency settings.
  5. Plot the components of complex exponentials, including an example with exponential amplitude decay.

Results & observations

m = 4.8 × 10⁻⁵ kgMechanical input parameters

The MATLAB model uses spring stiffness k = 800 N/m and damping coefficient c = 0.39 as documented.

0.01 sTransient plotting window

The provided code calls step and impulse for the stated model over this interval.

Impulse, step and sinusoidDiscrete signal examples

The report supplies MATLAB code and stem plots for these sequence families.

3e⁻ᵗᐟ²eʲ⁸ᵗDamped signal example

The supplied MATLAB code evaluates the complex exponential from 0 to 4 seconds.

Features & capabilities

  • Mechanical transfer-function model
  • Step and impulse plotting
  • Discrete-time stem plots
  • Frequency-parameter comparisons
  • Complex signal decomposition
  • Damped exponential visualization

Software & engineering tools

MATLAB, Control System Toolbox functions, tf, step, impulse, stem, real / imag / abs / angle

More engineering to explore.

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