SME3701 Assignment 01 2026 |Solid Mechanics IV| Due May 2026

UNIVERSITY OF SOUTH AFRICA (UNISA)
College of Science, Engineering and Technology



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ASSIGNMENT 01
Semester 1 — 2026


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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

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