Physics - Periodic Motion - High School and AP Physics

Explore how a simple pendulum can exhibit simple harmonic motion at angles, where restoring force follows sin theta rather than theta and sin theta ≈ theta up to 15 degrees.

Explore how a simple pendulum's period depends on length and gravity, with mass having negligible effect, and observe how angle and gravity alter the period.

Explore how a simple pendulum's period depends on length and gravity, with angle limited to 15 degrees and frequency inversely related, using T = 2π sqrt(L/g).

Explore how simple harmonic motion maps to uniform circular motion and waves by showing pendulum, mass-spring, and rotating platform systems with the same period, highlighting amplitude, equilibrium, and x positions.

Show how simple harmonic motion follows a cosine curve, linking displacement and time through period and pi, while velocity peaks at equilibrium and force and acceleration peak at the ends.

Explore uniform circular motion and its x and y components, using a radius as amplitude, deriving x = a cos theta to connect unit circle intuition with SHM.

Explore how SHM uses x = a sin(ωt) or x = a cos(ωt) with correct initial conditions, and apply θ = ωt and radian–degree conversions.

Analyze simple harmonic motion of a 1.15 kg mass on a spring with x = A cos(ωt); find A = 0.65 m, f = 1.34 Hz, E ≈ 17.1 J.

Explore the relationships among simple harmonic motion, velocity, acceleration, and waves in circular motion, using a spring‑mass model to link displacement, amplitude, and trig functions.

Damped harmonic motion causes amplitude to decay due to energy loss, while the period and frequency stay constant; includes under, critical, and over damping with examples like buildings and instruments.

Explore simple harmonic motion with spring and pendulum models, linking amplitude, equilibrium, velocity, acceleration, and energy, and show the period depends on mass and k, not amplitude or gravity.

Examines simple harmonic motion with single and parallel springs, shows how doubling spring constant shortens the period, and applies pendulum formulas to relate period to length and gravity.

Explore simple harmonic motion through pendulum geometry and spring energy, deriving height and velocity with theta, l, and cosine, and analyze energy transfer and period, and measure mass and period.

Explore simple harmonic motion of a mass on a spring, derive speed at equilibrium via energy conservation, and examine kinetic and potential energy and period changes.

Explore how potential and kinetic energy graphs relate to periodic motion in springs and pendulums, especially how kinetic energy peaks at the equilibrium position, then determine periods and amplitudes.

Use energy conservation in SHM to find amplitude and k, then state max speed and the general position forms x = A cos(ωt) or x = A sin(ωt).

Analyze a mass-spring system in simple harmonic motion using a kinetic-energy versus position graph to determine amplitude, maximum speed, and the spring constant, and relate total, kinetic and potential energies.

A clay hits a pendulum and sticks, illustrating momentum conservation and energy transfer in an inelastic collision. The lecture then covers the pendulum's period, system energy, and a break at the lowest point leading to a projectile range of about 0.72 meters.

Two blocks collide and stick, causing the combined mass to oscillate in simple harmonic motion. Momentum conservation yields post-collision speed, and energy balance gives amplitude and period 2 pi sqrt((M+m)/k).

Explore the sinusoidal motion of a mass on a spring, derive the position-time equation, and analyze period, angular frequency, amplitude, and how mass, spring constant, and amplitude affect the motion.

Analyze the sinusoidal nature of simple harmonic motion by deriving period, frequency, and angular frequency from a position-time graph, and compute amplitude, spring constant, energy, and max speed.