0113 Lecture Notes - AP Physics 1 Review of Simple Harmonic Motion.docx page 1 of 2

Flipping Physics Lecture Notes: AP Physics 1 Review of Simple Harmonic Motion

https://www.flippingphysics.com/ap1-shm-review.html

AP® is a registered trademark of the College Board, which was not involved in the production of, and does not endorse, this product. The mass-spring system shown at right is in simple harmonic motion. The mass moves through the following positions: 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, etc. Simple Harmonic Motion (SHM) is caused by a Restoring Force:

- A Restoring Force is always: o Towards the equilibrium

position. o Magnitude is proportional

to distance from equilibrium position.

To derive the equation for position in SHM, we start by comparing simple harmonic motion to circular motion.

&

(letting r = A) Looking at the graphs …

cosθ = A

H= x

r⇒ x = r cosθ

T = 2π

ω= 1

f⇒ω = 2π f

ω = Δθ

Δt=θ

f−θ

i

tf− t

i

=θ

f− 0

tf− 0

= θt⇒θ =ωt

x = r cosθ = r cos ωt( ) = r cos 2π f( ) t( )⎡⎣ ⎤⎦ = Acos 2π f( ) t( )⎡⎣ ⎤⎦

0113 Lecture Notes - AP Physics 1 Review of Simple Harmonic Motion.docx page 2 of 2

The period of a mass-spring system: Is independent of amplitude and acceleration due to gravity.

The period of a pendulum: Is independent of amplitude and mass.

T

s= 2π m

k

T

p= 2π L

g