{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chapter13

Chapter13 - Chapter 13 Lecture Essential University Physics...

This preview shows pages 1–9. Sign up to view the full content.

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

View Full Document

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

View Full Document

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

View Full Document

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

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

Unformatted text preview: Chapter 13 Lecture Essential University Physics Richard Welfsen 2nd Edition Oscillatory Motion Oscillatory Motion - A system in oscillatory motion undergoes repeating, periodic motion about a point of stable equilibrium. Hulh Iliulium haw the sum: period T - Oscillatory motion is {whim—Hm I characterized by Trainee-2r r—J- — Its frequency for period T=1/f. Period *l — Its amplitude A, or maximum excurSIon from equmbrlum. in Position - Shown here are position- versus-time graphs for two different oscillatory motions lg'gmﬂ fuel- with the same period and W :ﬂlfﬁi:ﬁfm amplitude. A ' ' Time Position :3 Simple Harmonic Motion - Simple harmonic motion (SHM) results when the force or torque that tends to restore equilibrium is directly proportional to the displacement from equilibrium. — The paradigm example is a mass m on a spring of spring constant k. - The angular frequency co = 2afor this system is J? m: E — In SHM, displacement is a sinusoidal function of time: I{F:]=AEDE{E1H+¢5:] Displacement. .r — Any amplitude A is possible. _,.. - In SHM, frequency doesn’t depend 'l'iilwniii . "'L‘l't'nLL'l]. lll'.:_ —.' . op “amplitude. “ "F-‘u’lr‘d’l 'innpnﬁnl: “a. : ru:_l_ an. n Quantities in Simple Harmonic Motion - Angular frequency, frequency, period: m=EEf=JHm Iii/E 22%:3‘]? - Phase — Describes the starting time of the displacement-versus- time curve in oscillatory motion: x(t) = Acos(ra t + gal) Displacement, J: Other Simple Harmonic Oscillators - The torsional oscillator — A fiber with torsional constant arc provides a restoring torque. — Frequency depends on K'Ell'ld rotational inertia: _ - Simple pendulum — Point mass on massless cord of length L: J? E T=2E — t 3 t I : mL - l"ir:|'.'its=.linlt;ll r'nniL' 7|l'l‘-H'.l|.1|._‘l:_'3~ i11l!l'-L]l|-L‘ I'Jntiuzliludu 3* U a T=£=EE i moiminii'. Ell mg}; ']'h:n:‘.~; no torque f'l'nm ll‘iL: lunh'un it Iwi'unw Ii :1th “innit: this. linL! in tin: pit-til. SHM and Circular Motion - Simple harmonic motion can be viewed as one component of uniform circular motion. — Angular frequency a) in SHM is the same as angular velocity (u in circular motion. [an I [hi I r I As the position vector F traces out a circle, its x— and y— components are a sinusoidal functions of time. Energy in Simple Harmonic Motion In the absence of nonconservative forces, the energy of a simple harmonic oscillator does not change. — But energy is transfered back and forth between kinetic and potential lincrg :r' forms. 1 E E=Tizd Clll.'l'}_'_1-' f' it run-Hill". .. _ . taili :' |1I||I.‘l"!'.'l| L'I'L'|'_-'._'~ |'-' i anJ kill:l£;£|i:.‘l'_ll_";.' H-ﬂiﬂlléﬂ. Energy 'I'ime Pentium l L" K I i h-ﬂ'lj'tl-jI-Eﬂ [I H # we 3 imam L" K . lﬂ'ﬂiiilj . -\._I F I _ w: w liliﬂiiliﬂ if K - liliiigﬂﬂ ."II J] . Ila-J ' W - li.i::i:.-i;i-:1t:J u liftiii-iita-ii‘d'lj i," a" I I F I l' -— [J m = Muser-1E L" K Equihbrium .I. = U TEEIIIIS'F'un-u-Edmultn I1.- Damped Harmonic Motion - With nonconseryatiye forces present, SHM gradually clamps out: m diff : all: air {it — Amplitude declines exponentially toward zero: — For weak damping b, oscillations still occur at approximately the undamped frequency — With stronger damping, oscillations cease. - Critical damping brings the system to equilibrium most quickly. Thu object still oscillates sinusoidally . . . L... E s s U _ E % Tli‘i‘ic, i" E U E El E all a A ' ' _ _ _ . . . but llic illll|3]llL|Ll|: Llcci'caiscs (a) Underdamped, Grltlcally dampEd, williiii [l1u“u:n-u|npu"ul'u and (c) oyerdamped oscillations. “mil”?L‘llllillmlml Resonance - When a system is driven by an external force at near its natural frequency, it responds with large-amplitude oscmaﬂons. — This is the phenomenon of resonance. — The size of the resonant response increases as damping decreases. — The width of the resonance curve (amplitude versus driving frequency) also narrows with lower damping. till” (1' J: m t =—t::— b—+Fﬁcosmdr air air Resonance curves for several damping strengths; we] is the undamped natural frequency ﬁlk/m Amplitude. rt ['J'J'H 2m“ 3-H)” Driving I‘rcqucncy. rod ...
View Full Document

{[ snackBarMessage ]}

Page1 / 9

Chapter13 - Chapter 13 Lecture Essential University Physics...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online