AP Physics 1: Complete Guide to Periodic Motion and SHM

Simple Harmonic Motion (SHM)

Oscillatory motion where the restoring force is proportional and opposite to displacement.

Restoring Force Condition

Condition for SHM defined as F_restoring = -kx.

Period (T)

The time it takes to complete one full cycle of motion.

Frequency (f)

The number of cycles completed per second.

Amplitude (A)

The maximum displacement from the equilibrium position.

Displacement (x)

Position relative to the equilibrium point, where x=0.

Angular frequency (ω)

Measure of rotation rate or oscillation speed expressed as 2πf.

Kinematics of SHM

Study of position, velocity, and acceleration as functions of time in SHM.

Sinusoidal wave

The graphical representation of position in SHM over time.

Maximum velocity (vmax)

The highest speed of the object at the equilibrium position in SHM.

Maximum acceleration (amax)

The highest acceleration occurs at maximum displacement in SHM.

Mass-Spring System

A classic example of SHM where a mass is attached to a spring.

Period of a spring (Ts)

The period given by Ts = 2π√(m/k).

Inertial properties (mass)

The property that affects how much an object resists acceleration.

Restoring properties (spring stiffness)

The property that defines how strong the force exerted by a spring is.

Vertical spring equilibrium position

The new equilibrium position when a spring is stretched by gravity.

Simple Pendulum

A pendulum consisting of a bob of mass attached to a frictionless string.

Restoring force in a pendulum

The component of gravity acting tangent to the arc of motion.

Small Angle Approximation

Assumption that sin(θ) is approximately equal to θ for small angles.

Period of a pendulum (Tp)

The period given by Tp = 2π√(L/g).

Mass independence in pendulum

The period of a pendulum does not depend on the mass of the bob.

Energy in SHM

The total mechanical energy in SHM is conserved and is a sum of kinetic and potential energies.

Potential Energy (Us)

Stored energy in a spring or gravitational field, defined as Us = 1/2 kx².

Kinetic Energy (K)

The energy of motion, defined as K = 1/2 mv².

Total Mechanical Energy (ET)

The sum of kinetic and potential energy, remains constant in SHM.

Energy Well

A parabolic graph representing the potential and kinetic energy vs. position.

Equilibrium position

The point where the net force acting on the system is zero.

Turning points in SHM

Points where velocity is zero, and acceleration is at its maximum.

Frequency vs. Period

Frequency is the number of cycles per second, while period is the time for one cycle.

Kinematic Equations Trap

The error of using kinematic equations where constant acceleration is not present.

Amplitude and Period relationship in SHM

Amplitude does not affect the period of SHM; they are independent.

Graphical analysis in SHM

The relationship between position, velocity, and acceleration over time.

Maximum displacement in SHM

Occurs at positions x = ±A where kinetic energy is zero.

Force in SHM

The restoring force that changes with position; higher at greater displacement.

Potential Energy at maximum displacement

All potential energy at x = ±A and zero kinetic energy.

Velocity at equilibrium

Maximum at equilibrium position (x = 0) with zero displacement.

Key variables in SHM

Period (T), Frequency (f), Amplitude (A), Displacement (x), Angular Frequency (ω).

Common mistakes in SHM

Confusing concepts like acceleration and velocity, or frequency and period.

Frequency mnemonics

Remember that frequency indicates speed (cycles per second) versus period as time.

Energy vs Position graph in SHM

Shows how energy is distributed between kinetic and potential as the object oscillates.

Kinematic equations limitation

Useful only for constant acceleration; SHM involves variable acceleration.

Pendulum mass confusion

Misconception that heavier pendulums swing faster; period independent of mass.

Spring and gravitational forces

Gravity shifts the equilibrium position but does not affect the period of a spring.

SHM examples

Mass-spring systems and simple pendulums are common real-world examples of SHM.

Equilibrium shifting

In vertical springs, equilibrium shifts by an amount Δx = mg/k.

Non-linear restoring force effects

Forces not proportional to displacement cannot yield SHM.

Energy conservation in SHM

Assuming no friction, total energy remains constant throughout oscillation.