T ā 2Ļ ā(L/g)T: s; L: m; g: m/sĀ².
Use when: Small angular amplitudes, point mass and negligible friction.
The simple pendulum
Relate the oscillation period to the length of the wire and gravity.
What is happening?
A pendulum exchanges gravitational potential energy and kinetic energy. In the ideal model, the wire is inextensible, its mass is neglected and friction is absent.
At small angles, the movement is close to a harmonic oscillation. The period depends on the length and severity; the simple formula becomes less precise as the amplitude increases.
The formulas, with their conditions.
E = Ā½mvĀ² + mghE: J; m: kg; v: m/s; h: m compared to a reference level.
Use when: Mechanical energy conserved in the absence of dissipation.
Where is this principle used?
Metrology workshop
Study oscillations and measure a period.
Sensor and instrument industry
Understand certain pendulum systems and the measurement of gravity.
What to observe in the experiment
Multiply the length by four without changing the gravity. Predict then measure the ratio of periods.
References and readings
This sheet explains the principles and their assumptions. Educational simulation can simplify the process; an industrial model requires suitable data and validation.
Have you understood the essentials?
Only one correct answer per question. Answer all three questions, then view the answer key.
Intu Lab Ā· Understanding sheet Ā· Kimba Christian