# Oscillations

## The Force Law for Simple Harmonic Motion

The Force Law for Simple Harmonic Motion Once we know how the acceleration of a particle varies with time, we can u Newton’s second law to learn what force must  ct on the particle to give it th acceleration. If we combine Newton’s second law and Eq. 16-8, we find, for simp, harmonic  otion, F = ma = -(I11W~)X. …

## PROBLEM·SOLVING TACTICS

PROBLEM·SOLVING TACTICS Note the effect of the phase angle 4> on a plot of x(l). When 4> = O, xCt) has a graph like that in Fig. 16-40. a typical cosine curve. Increasing 4> shifts the curve leftward along the taxis. (You might remember this with the symbol +4>. where the up arrow indicates an increase in 4> …

## The Acceleration of SHM

The Acceleration of SHM Knowing the velocity \1(/) for simple harmonic 1II0h0n’, we ( *l ~ 1ft. tat ••••• 1i for the acceleration of the oscillating particle by differenliMiD& .orp ~. have, from Eq. 16·6, d\~t) d . a(l) = -d-I = dt [-WX’” sm(WI +.t/J)] or a(t) = -w2xm COS(WI+ t/J) (acceleration). Figure 16-4c …

## The Velocity Of SHM

The Velocity Of SHM By differentiating Eq. 16-3, we can find an expression for the velocity of a particle moving with simple harmonic motion; that h s, dx(t) d v(t) = -‘ = – [x . ( ~OS(WI+ t/J)] dt dl m – (r) – Ag. 16-4 (a) The displacement *}of a particle oscillating in …

## Simple Harmonic Motion

Simple Harmonic Motion shows a sequence of “snapshots” of a simple oscillating system. a particle moving repeatedly back and forth about the origin of an x axis. I  this section we simply describe the motion. Later, we shall discuss how to attain such motion. One important property of oscillatory motion is its  requency, or number of oscillations that are …

## Oscillations

Oscillations We are surrounded by oscillations-motions that repeat themselves. There are swinging chandeliers. boats bobbing at anchor. and the surging pistons in the engines of cars. There are oscillating guitar strings, drums, bells,  iaphragms in telephones and speaker systems, and quartz crystals in  ristwatches. Less evident are the oscillations of the air molecules that transmit the sensation of sound. …