Edexcel A-Level Physics SHM Period Equations

Practise Edexcel A-Level Physics SHM period equations by calculating spring stiffness, pendulum length, frequency and mass changes.

Exam points

use T = 2π√(m/k) to calculate period, spring stiffness, mass or frequency
apply T = 2π√(l/g) to pendulum length, local gravity and period comparisons
deduce k from repeated oscillation timing or f² against inverse mass graphs

[Maximum number: 4]

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 5.5.145 - SHM period equations question 1 — Edexcel A-Level Physics A2

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 =

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5.5.145 - SHM period equations question 1