Edexcel A-Level Physics A2 5.5 Oscillations Questions

Practise Edexcel A-Level Physics oscillations through SHM conditions, displacement and velocity graphs, period equations, resonance, damping and oscillating-system energy.

Exam points

identify SHM from force or acceleration proportional to displacement toward equilibrium
use SHM period, velocity and acceleration equations with graphs and spring systems
explain resonance, damping and energy transfer in forced or free oscillations

Covered syllabus points

5.5.143 - Condition for simple harmonic motion 5.5.144 - SHM displacement, velocity and acceleration equations 5.5.145 - SHM period equations 5.5.146 - Displacement-time graphs for oscillations 5.5.147 - Velocity-time graphs for oscillations 5.5.148 - Resonance 5.5.149 - Core Practical 16 - unknown mass by resonance 5.5.150 - Energy conservation in oscillating systems 5.5.151 - Free and forced oscillations 5.5.152 - Resonance amplitude and damping 5.5.153 - Damping and plastic deformation

[Maximum number: 10]

The photograph shows the 60-storey John Hancock Tower in Boston. This is the tallest building in the state of Massachusetts in the USA.

Shortly after the building was completed in 1976 it was discovered that the wind caused the building to have large amplitude oscillations. To reduce the amplitude, a damper system was installed on the 58th floor.

The damper system consists of a lead box supported between springs, as shown below.

When the lead box is displaced, it moves with damped simple harmonic motion.

Figure for Question 1 — Edexcel A-Level Physics A2

(a)

State what is meant by simple harmonic motion.

[ 2 ]

(b)

When the wind blows at a certain speed, the building oscillates with a frequency of 0.17 Hz .

[ 6 ]

(i)

Explain why the damper system should be designed to oscillate at this frequency.

[ 2 ]

(ii)

The dimensions of the lead box are 5.20 m by 5.20 m by 0.90 m .

Calculate the stiffness of the spring system that attaches the lead box to the supports.
density of lead $=11300 \mathrm{~kg} \mathrm{~m}^{-3}$

Stiffness of spring system =

[ 4 ]

(c)

As the floor moves, the rollers force oil through holes in the steel plate.
Explain why this reduces the amplitude of oscillation of the building.

[ 2 ]

[Maximum number: 2]

A student added small lead spheres to a test tube. The student placed the test tube in a small beaker of water. The test tube floated as shown.

Figure for Question 2 — Edexcel A-Level Physics A2

The student gave the test tube a small vertical displacement. The test tube then oscillated vertically.

The student replaced the water with another liquid. The period is given by $T=\sqrt{\frac{16\pi m}{D^2\rho g}},$ where D is the test-tube diameter, m is the mass of the test tube and spheres, and $\rho$ is the liquid density.

Show that $\rho$ is about $1200\,\mathrm{kg\,m^{-3}}$ .

$D=2.38\pm0.01\,\mathrm{cm}$ , $T=0.61\pm0.01\,\mathrm{s}$ , $m=48.95\,\mathrm{g}$ .

Rearrange to $\rho=\frac{16\pi m}{D^2T^2g}.$ Substitution gives $\rho=\frac{16\pi(48.95\times10^{-3})}{(2.38\times10^{-2})^2(0.61)^2(9.81)}=1190\,\mathrm{kg\,m^{-3}},$ about $1200\,\mathrm{kg\,m^{-3}}$ .

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Covered syllabus points

Question 1

Question (a)

Question (b)

Question (i)

Question (ii)

Question (c)

Question 2