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Edexcel | Physics WPH0 | S 10 5 1 | 1 hour 30 minutes
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Read this passage and answer the questions that follow.

The Millennium Bridge opened on 10 June 2000 as London’s first new Thames

crossing in more than 100 years. The bridge uses “lateral suspension” – an engineeringinnovation that allows suspension bridges to be built without tall supporting columns. Tens of thousands of people crossed the bridge on its opening day.

The structure wasdesigned to take the weight, but suddenly the bridge began to sway and twist in regular oscillations. The worst of the movement occurred on the central span where the edge of the bridge oscillated through a total distance of 70 mm.

                         

To solve the problem the engineers decided to use damping mechanisms – giant shockabsorbers to limit the bridge’s response to external forces. They decided to use twosystems: viscous dampers, similar to car shock absorbers, and tuned mass dampers.

A tuned mass damper is a large mass stiffened by springs.

18
(a)
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2 Mark s

Name the effect that results in a system being driven into large amplitude

oscillations, and state the condition necessary for this to happen.

Resonance (1)

System driven at / near its natural frequency

18
(b)
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The graph shows the variation of velocity with time at the edge of the central span

of the bridg

Mark on this graph:

 

 

18
(b) (I)
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1 Mark

An instant X at which the displacement was a maximum.

 

Any zero velocity point

18
(b) (II)
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An instant Y at which the acceleration was zero.

Any maximum/minimum velocity point

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(c)
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Before modification the edge of the central span of the bridge oscillated with simple

maximum velocity of the edge of the central span of the bridge.

 

                                                 Maximum velocity = ....................................

 

18
(d)
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3 Mark s

The photograph shows the tuned mass dampers which were fitted to the bridge.

They are tuned to the natural frequency of oscillation of the bridge.

           

Discuss how the tuned mass dampers reduce the amplitude of the oscillations of the bridge and explain why they must be very heavily damped.

The answer must be clear and be organised in a logical sequence

The springs/dampers absorb energy (from the bridge) (1)

(Because) the springs deform/oscillate with natural frequency of the

bridge (1)

Hence there is an efficient/maximum transfer of energy (1)

Springs/dampers must not return energy to bridge / must dissipate

the energy

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