Simple Harmonic Motion

Simple Harmonic Motion

Motion where the restoring force is proportional to displacement.

Hooke’s Law

F = -kx

What is k?

Spring constant

What is x?

Displacement

What is A?

Amplitude

Potential Energy of a Spring

PE = 1/2kx²

Periodic Motion

Motion that repeats at regular intervals

Period

The time to complete one oscillation (T)

Frequency

The amount of oscillations per unit time (Hz)

Period Equation (Spring)

T = 2π√m/k

Frequency Equation

f = 1/T

If energy is conserved, the oscillator will have equal _______ on both sides of equilibrium.

Displacement (X)

Period is independent of ? (spring)

Amplitude (A)

Period is independent of ? (pendulum)

Mass & Amplitude

Period Equation (Pendulum)

T = 2π√L/g

Position Equation

x(t) = A cos(2πft)

Where is V the smallest?

At the amplitudes

Where is V the greatest?

At the equilibrium point