物理双语教学课件Chapter9Oscillations振动

Chapter 9 Oscillations

We are surrounded by oscillations─motions that repeat themselves. (1). There are swinging chandeliers, boats bobbing at anchor, and the surging pistons in the engines of cars. (2). There are oscillating guitar strings, drums, bells, diaphragms in telephones and speaker systems, and quartz crystals in wristwatches. (3). Less evident are the oscillations of the air molecules that transmit the sensation of sound, the oscillations of the atoms in a solid that convey the sensation of temperature, and the oscillations of the electrons in the antennas of radio and TV transmitters.

Oscillations are not confined to material objects such as violin strings and electrons. Light, radio waves, x-rays, and gamma rays are also oscillatory phenomena. You will study such oscillations in later chapters and will be helped greatly there by analogy with the mechanical oscillations that are about to study here.

Oscillations in the real world are usually damped; that is, the motion dies out gradually, transferring mechanical energy to thermal energy by the action of frictional force. Although we cannot totally eliminate such loss of mechanical energy, we can replenish the energy from some source.

Simple Harmonic Motion

1. The figure shows a sequence

of “snapshots” of a simple

oscillating system, a particle

moving repeatedly back and

forth about the origin of the x

axis.

2. Frequency: (1). One important

property of oscillatory motion

is its frequency , or number of

oscillations that are

completed each second . (2). The symbol for frequency is f, and (3) its SI unit is hertz (abbreviated Hz), where 1 hertz = 1 Hz = 1 oscillation per second = 1 s -1.

3. Period: Related to the frequency is the period T of the motion,

which is the time for one complete oscillation (or cycle). That is f T 1

=.

4. Any motion that repeats itself at regular intervals is called

period motion or harmonic motion . We are interested here in motion that repeats itself in a particular way. It turns out that for such motion the displacement x of the particle from the origin is given as a function of time by

)cos()(φω+=t x t x m , in

which φωand x m ,, are constant. The motion is called simple harmonic motion (SHM), the term that means that the periodic motion is a sinusoidal of time .

5. The quantity m x , a positive constant whose value depends on

how the motion was started, is called the amplitude of the motion; the subscript m stands for maximum displacement of the particle in either direction.

6. The time-varying quantity )(φω+t is called the phase of the

motion, and the constant φ is called the phase constant (or phase angle ). The value of φ depends on the displacement and velocity of the particle at t=0.

7. It remains to interpret the constant ω. The displacement )(t x

must return to its initial value after one period T of the motion. That is, )(t x must equal

)(T t x + for all t. To simplify our analysis, we put 0=φ. So we then have

)](cos[cos T t x t x m m +=ωω. The cosine function first repeats itself when its argument (the phase) has increased by π2 rad, so that we must have

πωπωω22)(=+=+T or t T t . It means f T ππω22==. The quantity ω is called the angular frequency of the motion; its SI unit is the radian per second.

8. The velocity of SHM: (1). Take derivative of the

displacement with time, we can find an expression for the