Practise Edexcel A-Level Physics oscillations through SHM conditions, displacement and velocity graphs, period equations, resonance, damping and oscillating-system energy.
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.
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.
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
Stiffness of spring system =
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.
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{ rac{16\pi m}{D^2 ho g}}, where D is the test-tube diameter, m is the mass of the test tube and spheres, and ho is the liquid density.
Show that ho is about .
, , .