lecture34 - Harmonic Motion III • Simple and Physical...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Harmonic Motion ( III ) • Simple and Physical Pendulum • SHM and uniform circular motion Simple Pendulum Gravity is the “restoring force” taking the place of the “spring” in our block/spring system. Instead of x, measure the displacement as the arc length s along the circular path. Write down the tangential component of F=ma: θ sin mg = L θ T θ θ θ θ sin But ) sin( 2 2 2 2 L g dt d L s mg ma dt s d m t- = ⇒ =- = = mg sin θ Restoring force s mg θ θ sin 2 2 L g dt d- = Simple pendulum: x dt x d 2 2 2 ϖ- = SHM: The pendulum is not a simple harmonic oscillator! θ θ θ L g L g dt d- ≈- = sin 2 2 θ θ 2245 sin However, take small oscillations: (radians) if θ is small. Then This looks like L g = ϖ θ θ L g dt d- = 2 2 For small θ : x dt x d 2 2 2 ϖ- = , with angle θ instead of x . The pendulum oscillates in SHM with an angular frequency and the position is given by ) cos( ) ( o φ ϖ θ θ + = t t amplitude phase constant (2 π / period) • a simple harmonic oscillator is a mathematical ‘approximation’ to the full problem • for large amplitudes, the solution that the SHO gives...
View Full Document

{[ snackBarMessage ]}

Page1 / 18

lecture34 - Harmonic Motion III • Simple and Physical...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online