UNIVERSITY OF SOUTH AFRICA (UNISA)
College of Science, Engineering and Technology
⋄
ASSIGNMENT 01
Semester 1 — 2026
⋄
Module Code: SME3701
Module Name: Solid Mechanics IV
Assignment No.: 01
Due Date: 2026
Semester: Semester 1, 2026
Submitted in partial fulfilment of the requirements for Solid Mechanics IV
at the University of South Africa.
, UNISA | SME3701 Solid Mechanics IV — Assignment 01
Question 1: Undamped Free Vibration of a Mass–Spring System [22 marks]
Consider a single-degree-of-freedom (SDOF) mass–spring system undergoing undamped free
vibration, as illustrated in Figure 1. The system consists of a mass of 5 kg attached to a spring
with stiffness 2000 N/m. The system is initially displaced by 0.02 m and released from rest
with zero initial velocity. The motion of the system is described by the equation:
x(t) = x0 cos(ωn t)
where ωn is the natural angular frequency.
k
m x(t)
m = 5 kg, k = 2000 N/m, x0 = 0.02 m
Figure 1: Undamped Free Vibration of a Mass–Spring System.
1.1 Natural Angular Frequency using MATLAB [3 marks]
Question: Determine the natural angular frequency ωn of the system using MATLAB.
Step 1: Recall the formula for natural angular frequency.
For an undamped SDOF system, the natural angular frequency is defined as (Rao, 2017:134):
r
k
ωn =
m
Step 2: Substitute the known values.
Given: k = 2000 N/m and m = 5 kg.
2000 √
r
ωn = = 400 = 20 rad/s
5
Page 1 of 10
College of Science, Engineering and Technology
⋄
ASSIGNMENT 01
Semester 1 — 2026
⋄
Module Code: SME3701
Module Name: Solid Mechanics IV
Assignment No.: 01
Due Date: 2026
Semester: Semester 1, 2026
Submitted in partial fulfilment of the requirements for Solid Mechanics IV
at the University of South Africa.
, UNISA | SME3701 Solid Mechanics IV — Assignment 01
Question 1: Undamped Free Vibration of a Mass–Spring System [22 marks]
Consider a single-degree-of-freedom (SDOF) mass–spring system undergoing undamped free
vibration, as illustrated in Figure 1. The system consists of a mass of 5 kg attached to a spring
with stiffness 2000 N/m. The system is initially displaced by 0.02 m and released from rest
with zero initial velocity. The motion of the system is described by the equation:
x(t) = x0 cos(ωn t)
where ωn is the natural angular frequency.
k
m x(t)
m = 5 kg, k = 2000 N/m, x0 = 0.02 m
Figure 1: Undamped Free Vibration of a Mass–Spring System.
1.1 Natural Angular Frequency using MATLAB [3 marks]
Question: Determine the natural angular frequency ωn of the system using MATLAB.
Step 1: Recall the formula for natural angular frequency.
For an undamped SDOF system, the natural angular frequency is defined as (Rao, 2017:134):
r
k
ωn =
m
Step 2: Substitute the known values.
Given: k = 2000 N/m and m = 5 kg.
2000 √
r
ωn = = 400 = 20 rad/s
5
Page 1 of 10
