A Chapter 17 Oscillations
Chapter 17 Oscillations
17-1 Oscillating Systems Each day we encounter many kinds of oscillatory a motion, such as swinging pendulum of a clock, a person bouncing on a trampoline, a vibrating guitar string, and a mass on a spring e They have common properties 1. The particle oscillates back and forth about a equilibrium position. The time necessary for one complete cycle (a complete repetition of the motion)is called the period I
17-1 Oscillating Systems Each day we encounter many kinds of oscillatory motion, such as swinging pendulum of a clock, a person bouncing on a trampoline, a vibrating guitar string, and a mass on a spring. They have common properties: 1. The particle oscillates back and forth about a equilibrium position. The time necessary for one complete cycle (a complete repetition of the motion) is called the period T
2. No matter what the direction of the displacement the force always acts in a direction to restore the system to its equilibrium position. Such a force is called a" restoring force(恢复力) 3. The number of cycles per unit time is called the ●“ frequency (17-1) Unit: period(s) frequency (Hz, sI unit), 1 Hz =1 cycle/s 4. The magnitude of the maximum displacement from equilibrium is called the amplitude of the motion
2. No matter what the direction of the displacement, the force always acts in a direction to restore the system to its equilibrium position. Such a force is called a “restoring force(恢复力)”. 3. The number of cycles per unit time is called the “frequency” f. (17-1) Unit: period (s) frequency(Hz, SI unit), 1 Hz = 1 cycle/s T f 1 = 4. The magnitude of the maximum displacement from equilibrium is called the amplitude of the motion
17-2/3 The simple harmonic oscillator and its motion 1. Simple harmonic motion An oscillating system which can be described in e terms of sine and cosine functions is called a "simple harmonic oscillator" and its motion is called e simple harmonic motion". 2. Equation of motion of the simple harmonic oscillator Fig 17-5 shows a simple harmonic oscillator consisting of a spring of force constant K acting on
17-2/3 The simple harmonic oscillator and its motion 1. Simple harmonic motion An oscillating system which can be described in terms of sine and cosine functions is called a “simple harmonic oscillator” and its motion is called “simple harmonic motion”. 2. Equation of motion of the simple harmonic oscillator Fig 17-5 shows a simple harmonic oscillator, consisting of a spring of force constant K acting on
a body of mass m that slides on a frictionless horizontal e surface. the body moves in x direction Fg17-5 origin is chosen at here Relaxed state ∑F=-k 2 -kx= m k (17-4)
a body of mass m that slides on a frictionless horizontal surface. The body moves in x direction. Fig 17-5 x x m m F o o • • Relaxed state origin is chosen at here F kx x = − 2 2 dt d x ax = 2 2 dt d x − kx = m 0 2 2 + x = m k dt d x (17-4)