PHY26041/102/0/2026 0793226427
UNISA
PHY2604 Assignment 1 full solutions 2026
Unique code: 197355
Due Date: 30 April 2026
This the Actual Experiments that will be conducted at Florida
campus, this document contains, even some note to help you
understand the experiments in advance, reach me for written lab
reports pdfs, so that you will be familiar with the report’s structures
, Driven Harmonic Oscillator
Question 1 — Resonance
Resonance occurs when a system is driven at its natural frequency, causing the amplitude of
oscillation to reach a maximum.
Question 2 — Aluminium Disk
Given: density ρ = 8 g/cm³, thickness h = 20 mm = 2 cm, diameter = 135 mm → radius R = 67.5
mm = 6.75 cm
(a) Radius: R = 135/2 = 67.5 mm = 0.0675 m
(b) Moment of Inertia:
First find the mass:
• Volume = πR²h = π × (6.75)² × 2 = π × 45.5625 × 2 = 286.28 cm³
• Mass = ρV = 8 × 286.28 = 2290.2 g = 2.290 kg
Moment of inertia of a solid disk:
1 1
𝐼= 𝑀𝑅 2 = × 2.290 × (0.0675)2
2 2
𝐼 = 5.21 × 10−3 kg.m2
Question 3 — Weight and Torque
Weight of 750 g mass:
𝑊 = 𝑚𝑔 = 0.750 × 9.8 = 7.35 N
Torque with pulley radius r = 33 cm = 0.33 m:
𝜏 = 𝐹 × 𝑟 = 7.35 × 0.33 = 2.43 N\cdotpm
2
, PHY26041/102/0/2026 0793226427
Question 4 — Sources of Torque on the Disk
1. Driving torque — applied externally (e.g., via the string/pulley system) that forces the disk
to oscillate.
2. Damping torque — opposes motion, arising from air resistance or magnetic braking (eddy
currents), proportional to angular velocity. (A third one: restoring torque from the torsional
spring/wire.)
Question 5 — From Figure 2
From the damped oscillation graph:
• Period T ≈ read two successive peaks; the oscillations appear to have T ≈ 6–7 s (estimate
from graph)
• Damped angular frequency: ω_d = 2π/T ≈ 2π/6.5 ≈ 0.97 rad/s
For the damping constant γ, use the envelope decay. The amplitude decays as e^(−γt/2).
Reading two amplitudes at different times from the envelope gives γ. From the graph, amplitude
drops from ~1 to ~0.5 in roughly t ≈ 14 s:
2ln 2
𝑒 −𝛾⋅14/2 = 0.5 ⇒ 𝛾 = ≈ 0.099 s−1
14
Natural (undamped) frequency:
𝛾 2
𝜔0 = √𝜔𝑑2 + ( ) ≈ √(0.97)2 + (0.05)2 ≈ 0.97 rad/s
2
(nearly equal to ω_d since damping is light)
UNISA
PHY2604 Assignment 1 full solutions 2026
Unique code: 197355
Due Date: 30 April 2026
This the Actual Experiments that will be conducted at Florida
campus, this document contains, even some note to help you
understand the experiments in advance, reach me for written lab
reports pdfs, so that you will be familiar with the report’s structures
, Driven Harmonic Oscillator
Question 1 — Resonance
Resonance occurs when a system is driven at its natural frequency, causing the amplitude of
oscillation to reach a maximum.
Question 2 — Aluminium Disk
Given: density ρ = 8 g/cm³, thickness h = 20 mm = 2 cm, diameter = 135 mm → radius R = 67.5
mm = 6.75 cm
(a) Radius: R = 135/2 = 67.5 mm = 0.0675 m
(b) Moment of Inertia:
First find the mass:
• Volume = πR²h = π × (6.75)² × 2 = π × 45.5625 × 2 = 286.28 cm³
• Mass = ρV = 8 × 286.28 = 2290.2 g = 2.290 kg
Moment of inertia of a solid disk:
1 1
𝐼= 𝑀𝑅 2 = × 2.290 × (0.0675)2
2 2
𝐼 = 5.21 × 10−3 kg.m2
Question 3 — Weight and Torque
Weight of 750 g mass:
𝑊 = 𝑚𝑔 = 0.750 × 9.8 = 7.35 N
Torque with pulley radius r = 33 cm = 0.33 m:
𝜏 = 𝐹 × 𝑟 = 7.35 × 0.33 = 2.43 N\cdotpm
2
, PHY26041/102/0/2026 0793226427
Question 4 — Sources of Torque on the Disk
1. Driving torque — applied externally (e.g., via the string/pulley system) that forces the disk
to oscillate.
2. Damping torque — opposes motion, arising from air resistance or magnetic braking (eddy
currents), proportional to angular velocity. (A third one: restoring torque from the torsional
spring/wire.)
Question 5 — From Figure 2
From the damped oscillation graph:
• Period T ≈ read two successive peaks; the oscillations appear to have T ≈ 6–7 s (estimate
from graph)
• Damped angular frequency: ω_d = 2π/T ≈ 2π/6.5 ≈ 0.97 rad/s
For the damping constant γ, use the envelope decay. The amplitude decays as e^(−γt/2).
Reading two amplitudes at different times from the envelope gives γ. From the graph, amplitude
drops from ~1 to ~0.5 in roughly t ≈ 14 s:
2ln 2
𝑒 −𝛾⋅14/2 = 0.5 ⇒ 𝛾 = ≈ 0.099 s−1
14
Natural (undamped) frequency:
𝛾 2
𝜔0 = √𝜔𝑑2 + ( ) ≈ √(0.97)2 + (0.05)2 ≈ 0.97 rad/s
2
(nearly equal to ω_d since damping is light)
