Simple Pendulum Motion
A simple pendulum consists of a mass (bob) suspended from a fixed point by a massless string or rod. For small angles (less than 15 degrees), the period T = 2pisqrt(L/g), where L is length and g is gravitational acceleration. Remarkably, the period is independent of mass and amplitude (for small swings). This makes pendulums excellent timekeepers. A 1-meter pendulum on Earth has a period of about 2 seconds.
Pendulum Period and Frequency
Period is the time for one complete swing, while frequency is oscillations per second (f = 1/T). Longer pendulums swing slower with longer periods. Doubling length increases period by sqrt2 (about 41%). Grandfather clocks use pendulums typically 1 meter long with 2-second periods. The pendulum's independence from mass and amplitude (for small swings) made it ideal for timekeeping before electronic clocks. Even today, this principle appears in metronomes and seismometers.
Applications and Historical Significance
Galileo discovered pendulum properties in the 1600s, leading to the first accurate clocks. Pendulums determined gravitational acceleration in different locations. Foucault's pendulum demonstrated Earth's rotation. Engineers use pendulum principles in shock absorbers, seismographs, and tuned mass dampers in skyscrapers. Swings in playgrounds follow pendulum motion. Understanding pendulums helps design stable structures, improve timekeeping, and study oscillatory systems throughout physics and engineering.
Quick Tips
- Always verify units are consistent
- Use scientific notation for very large/small numbers
- Results are approximations — real conditions may vary
Frequently Asked Questions
No, for a simple pendulum with small angles, mass doesn't affect period. Both heavy and light pendulums of the same length have identical periods. This seems counterintuitive but was discovered by Galileo.
For small angles (< 15 degrees), the restoring force is nearly proportional to displacement, making it simple harmonic motion with amplitude-independent period. Large angles introduce nonlinearity, increasing the period slightly.
Period T ? 1/sqrtg. Stronger gravity means faster swings and shorter periods. A pendulum on the Moon (g = 1.62 m/s^2) swings much slower than on Earth.
A Foucault pendulum is a large, freely swinging pendulum that demonstrates Earth's rotation. The swing plane appears to rotate because Earth rotates beneath it. The rotation rate depends on latitude.
Yes, by measuring period and length, you can calculate g = 4pi^2L/T^2. Variations in Earth's gravity due to altitude, latitude, and underground density affect pendulum periods, allowing gravitational surveys.