Simple Harmonic Motion

Four topics build the physics of oscillation, from what makes motion repeat to where its energy goes. Defining simple harmonic motion identifies the one condition behind every oscillator: a restoring force proportional to displacement. Frequency and period set the timing of a spring or a pendulum, and reveal what the timing does and does not depend on. Representing and analyzing simple harmonic motion tracks position, velocity, and acceleration as they trade off a quarter cycle apart. Energy of simple harmonic oscillators follows the steady exchange between kinetic and potential energy as the system swings between its turning points.

Topics

7.1

Defining Simple Harmonic Motion

Frequency and Period of SHM

Representing and Analyzing SHM

Energy in Simple Harmonic Motion

Lesson

Diag

locked

Equations For every problem in this unit

Period and frequency

$T = \dfrac{1}{f}$

Spring oscillator period

$T_s = 2\pi\sqrt{\dfrac{m}{k}}$

Pendulum period (small swings)

$T_p = 2\pi\sqrt{\dfrac{\ell}{g}}$

Position, released from maximum

$x = A\cos(2\pi f t)$

Position, released from equilibrium

$x = A\sin(2\pi f t)$

Restoring force

$F_s = -k\,\Delta x$

Spring potential energy

$U_s = \tfrac{1}{2}k(\Delta x)^2$

Pythagorean

$a^2 + b^2 = c^2$

Sine, opp / hyp

$\sin\theta = \dfrac{a}{c}$

Cosine, adj / hyp

$\cos\theta = \dfrac{b}{c}$

Tangent, opp / adj

$\tan\theta = \dfrac{a}{b}$

Unit 7 tools

Challenge bank

1 / 60

60 open-ended problems.

Read the question, work it out, then flip the card to compare your reasoning to the worked solution. Mark each card so you can return to the ones that still bite.

Question

Tap card to reveal explanation

Worked solution

Tap card to return to question

Cumulative assessment

Test the unit.

Twenty mixed items pulled from across all 4 topics. Identifies which misconceptions still bite when you cannot see which topic the question came from.