SME3701
Assignment 02
Due Year 2025
, SME3701 Assignment 02 2025
Question 1 [28]
A team of mechanical engineers is tasked with analysing the dynamic behavior of a single-degree-
of-freedom (SDOF) mechanical system subjected to various forms of harmonic excitation. The goal
is to understand the system's steady-state response under different scenarios, including undamped
and damped conditions, base excitation, and rotating unbalance. The engineers are required to
simulate these cases using MATLAB and interpret the results through appropriate plots. The
mechanical system under investigation has a mass of m=10 kg and stiffness of k=4000 N/m.
Question 1.1
Write a MATLAB function to simulate and plot the steady-state response x(t) of an undamped
single-degree-of-freedom (SDOF) system subjected to a harmonic force F(t)=100cos(ωt). Evaluate
the system response over an excitation frequency range of ω=1 to 40 rad/s. Provide a brief
interpretation of the resulting plot. (7)
Matlab
function undamped_response()
% UNDAMPED_RESPONSE
% Plots the steady-state response amplitude of an undamped SDOF system
% under harmonic excitation.
%
% System parameters:
% m - mass (kg)
% k - stiffness (N/m)
% F0 - force amplitude (N)
% Parameters
m = 10; % Mass (kg)
k = 4000; % Stiffness (N/m)
F0 = 100; % Force amplitude (N)
% Natural frequency
omega_n = sqrt(k/m); % rad/s
% Frequency range
omega = linspace(1, 40, 1000); % rad/s
, % Steady-state amplitude
amplitude = F0 ./ abs(k - m .* omega.^2);
% Plot response
figure('Name','Undamped Response','NumberTitle','off');
plot(omega, amplitude, 'b', 'LineWidth', 1.5); hold on;
% Add resonance line
yMax = max(amplitude(~isinf(amplitude))); % avoid Inf at resonance
plot([omega_n omega_n], [0 yMax], 'r--', 'LineWidth', 1.2);
% Labels and formatting
xlabel('Excitation Frequency \omega (rad/s)', 'FontSize', 12);
ylabel('Amplitude of Response x(t) (m)', 'FontSize', 12);
title('Steady-State Response Amplitude vs. Frequency (Undamped)' , 'FontSize',
14);
legend('Amplitude Response', 'Resonance Frequency', 'Location', 'northwest');
grid on;
box on;
hold off;
end
Output
Assignment 02
Due Year 2025
, SME3701 Assignment 02 2025
Question 1 [28]
A team of mechanical engineers is tasked with analysing the dynamic behavior of a single-degree-
of-freedom (SDOF) mechanical system subjected to various forms of harmonic excitation. The goal
is to understand the system's steady-state response under different scenarios, including undamped
and damped conditions, base excitation, and rotating unbalance. The engineers are required to
simulate these cases using MATLAB and interpret the results through appropriate plots. The
mechanical system under investigation has a mass of m=10 kg and stiffness of k=4000 N/m.
Question 1.1
Write a MATLAB function to simulate and plot the steady-state response x(t) of an undamped
single-degree-of-freedom (SDOF) system subjected to a harmonic force F(t)=100cos(ωt). Evaluate
the system response over an excitation frequency range of ω=1 to 40 rad/s. Provide a brief
interpretation of the resulting plot. (7)
Matlab
function undamped_response()
% UNDAMPED_RESPONSE
% Plots the steady-state response amplitude of an undamped SDOF system
% under harmonic excitation.
%
% System parameters:
% m - mass (kg)
% k - stiffness (N/m)
% F0 - force amplitude (N)
% Parameters
m = 10; % Mass (kg)
k = 4000; % Stiffness (N/m)
F0 = 100; % Force amplitude (N)
% Natural frequency
omega_n = sqrt(k/m); % rad/s
% Frequency range
omega = linspace(1, 40, 1000); % rad/s
, % Steady-state amplitude
amplitude = F0 ./ abs(k - m .* omega.^2);
% Plot response
figure('Name','Undamped Response','NumberTitle','off');
plot(omega, amplitude, 'b', 'LineWidth', 1.5); hold on;
% Add resonance line
yMax = max(amplitude(~isinf(amplitude))); % avoid Inf at resonance
plot([omega_n omega_n], [0 yMax], 'r--', 'LineWidth', 1.2);
% Labels and formatting
xlabel('Excitation Frequency \omega (rad/s)', 'FontSize', 12);
ylabel('Amplitude of Response x(t) (m)', 'FontSize', 12);
title('Steady-State Response Amplitude vs. Frequency (Undamped)' , 'FontSize',
14);
legend('Amplitude Response', 'Resonance Frequency', 'Location', 'northwest');
grid on;
box on;
hold off;
end
Output
