Simple Harmonic Motion
Mass on spring + pendulum side by side. Builds on Hooke's Law & Springs.
A grandfather clock with a 1-meter pendulum keeps perfect time on Earth. You take it to the Moon, where gravity is 1/6 of Earth's.
What happens to the clock on the Moon?
The period of a pendulum is T = 2π√(L/g). On the Moon, g is 6× smaller, so T increases by √6 ≈ 2.45×. The clock ticks about 2.4 times slower — not 6 times! The square root relationship is key.
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Watch a mass on a spring and a pendulum oscillate side by side. Adjust gravity and see the pendulum change while the spring stays the same!
T = 2π√(m/k)
The period doesn't depend on amplitude! Swing a pendulum gently or wildly — same period (for small angles). Galileo reportedly discovered this watching a chandelier in Pisa Cathedral.
A quartz crystal vibrates at exactly 32,768 Hz — that's SHM at the atomic level. Divide by 2¹⁵ and you get exactly 1 tick per second.
Taipei 101 has a 730-ton pendulum (tuned mass damper) that swings opposite to the building's oscillation, canceling wind-induced sway.
The SA node in your heart acts as a biological oscillator. Its electrical rhythm follows SHM principles — which is why EKGs show periodic waveforms.
“SHM is nature's favorite motion. From atomic vibrations to galactic wobbles, the universe oscillates. And it all comes from one simple law: F = −kx.”
Oscillation Lab
Compare a mass on a spring with a pendulum. Adjust mass, spring constant, length, and gravity to see how the period changes.
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Make the spring's period match the pendulum's period. Then change gravity — the pendulum changes but the spring doesn't! Springs don't care about gravity.
A spring's period depends on mass and stiffness. A pendulum's period depends on length and gravity. Neither depends on amplitude (for small oscillations).