The Rhythms of Nature

Many systems in physics oscillate—think springs, pendulums, or planetary orbits!

Simple Harmonic Motion (SHM)

Objects like springs and pendulums move in repetitive cycles described by SHM. Calculus allows us to model their position with sine and cosine functions.

• The restoring force is proportional to displacement: \( F = -kx \).
• The solution: \( x(t) = A \cos(\omega t + \phi) \).

Universal Gravitation

Newton's Law of Gravitation: \[ F = G\frac{m_1 m_2}{r^2} \] describes the attractive force between masses.

Orbits and Energy

Calculus is essential for analyzing elliptical orbits and gravitational potential energy.

Applications

Clocks, musical instruments, and satellites all rely on oscillatory motion and gravitation!