11-14-2025, 10:31 PM
[border]TIER 8 — Advanced Modelling[/border]
Tier 8 — Challenge 003 — The Harmonic Bridge Cable
A suspension bridge cable behaves approximately like a catenary:
y(x) = a cosh(x/a) − a
Where:
• y(x) is the height of the cable above its lowest point
• a = 65 metres
• x is horizontal distance from the centre
You are analysing vibrations in the cable caused by wind.
Questions:
1. What is the height difference between the centre (x = 0)
and a point 30 m horizontally away?
2. The tension at a point is approximately proportional to y(x).
Compare the tension at x = 30 m to the tension at the lowest point.
3. Explain whether the shape suggests higher or lower resonance risk
compared to a straight cable of equal length.
Show your reasoning as clearly as possible — this is Tier 8 depth.
? Submit Your Attempt
Thread title:
Tier 8 Attempt — YourUsername — Challenge 003
Tier 8 — Challenge 003 — The Harmonic Bridge Cable
A suspension bridge cable behaves approximately like a catenary:
y(x) = a cosh(x/a) − a
Where:
• y(x) is the height of the cable above its lowest point
• a = 65 metres
• x is horizontal distance from the centre
You are analysing vibrations in the cable caused by wind.
Questions:
1. What is the height difference between the centre (x = 0)
and a point 30 m horizontally away?
2. The tension at a point is approximately proportional to y(x).
Compare the tension at x = 30 m to the tension at the lowest point.
3. Explain whether the shape suggests higher or lower resonance risk
compared to a straight cable of equal length.
Show your reasoning as clearly as possible — this is Tier 8 depth.
? Submit Your Attempt
Thread title:
Tier 8 Attempt — YourUsername — Challenge 003