Edexcel A-Level Physics A2 5.5 Oscillations Questions

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.

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.

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 $1200\,\mathrm{kg\,m^{-3}}$.

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

A student set up a simple pendulum. The student used a velocity sensor connected to a data logger to record the velocity of the pendulum bob.

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.

State what is meant by simple harmonic motion.

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.

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

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 =

A student set up a simple pendulum. The student used a velocity sensor connected to a data logger to record the velocity of the pendulum bob.

The graph shows how the velocity of the bob varied with time.

Add a line to the graph to show how the displacement of the bob varied with time during the same time interval.

Questions 9 and 10 refer to the following information.
The graph shows how the velocity v varies with time t for an object performing simple harmonic motion.
Four graphs for the same period of time are shown below.
Which graph shows how the acceleration of the object varies with t?

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.

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

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

A student hangs a mass of 0.22 kg from two identical springs as shown.

She displaces the mass vertically and the mass oscillates with simple harmonic motion.

The student attaches the mass to one spring and holds the other end. She sets the mass into oscillation by oscillating her hand vertically, as shown.

The student increases the frequency at which she oscillates her hand. She keeps the amplitude of oscillation of her hand constant.

She observes that the amplitude of oscillation of the mass increases to a maximum and then decreases.

The student makes the following conclusion:
"As the frequency is increased, the amplitude of the mass increases to a maximum, so energy conservation does not apply to this situation."

Explain whether her conclusion is correct.

A mass is forced into oscillation by a vibration generator. After a short time the oscillation becomes steady.

Which of the following statements about the steady oscillation of the mass is always true?

A music system has a number of loudspeakers. One loudspeaker produces the low frequency sounds. This loudspeaker consists of a coil connected to a cone. The coil is in a region of magnetic field produced by a permanent magnet, as shown.

At a particular frequency, the loudspeaker cone starts to oscillate with a very large amplitude.

Explain why this effect is observed.

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.

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.