16.3 Simple Harmonic Motion: A Special Periodic Motion

16.3 Simple Harmonic Motion: A Special Periodic Motion

  • The period found in (b) is the time per cycle, but this value is often quoted as simply the time in convenient units.
  • You can identify an event in your life that occurs frequently.
  • The net force that can be described by Hooke's law is very common.
    • They are the simplest systems.
    • The units for displacement and amplitude are the same.
    • For the object on the spring, the units of amplitude and displacement are meters; whereas for sound oscillations, they have units of pressure.
    • The energy in the oscillation is related to the maximum displacement.
  • There is a bowl or basin that is shaped like a hemisphere.
    • Place a marble inside the bowl and tilt the bowl so the marble rolls from the bottom of the bowl to the high points on the sides of the bowl.
    • This periodic motion requires force to maintain it.
  • An object attached to a spring sliding on a surface is a simple harmonic oscillator.
    • The object performs simple motion when it is displaced from equilibrium.
    • As it passes through equilibrium, the object's maximum speed occurs.
    • The period is smaller when the spring is stiff.
    • The period is affected by the mass of the object.
  • There is a special thing about the period and frequencies of a simple harmonic oscillator.
    • The string of a guitar can be plucked gently or hard.
    • The period is constant, so a simple harmonic oscillator can be used as a clock.
  • There are two important factors that affect the period.
    • The period is related to how stiff the system is.
    • The system has a smaller period because of the stiff object.
    • You can adjust a diving board's stiffness, for example, if you want it to vibrate quicker.
    • Period is dependent on the mass of the system.
    • The longer the period, the bigger the system is.
    • A heavy person on a diving board bounces up and down more slowly than a light person.
  • The mass and force constant are the only factors that can affect the period and frequencies of simple motion.
  • There is no dependence on amplitude.
  • If you want the length of the ruler that protrudes from the table to be the same, tape one end of the ruler to the edge of the table.
  • Measure the period of oscillation of each of the rulers bylucking the ends of the rulers at the same time and observing which one undergoes more cycles in a time period.
  • The equation states that the car's oscillations will be similar to a simple harmonic oscillator.
    • The mass and force constant are given.
  • The values seem right for a bouncing car.
    • If you push down hard on the end of the car, you can see the oscillations.
  • Figure 16.11 shows an object bouncing on a spring as it leaves a wavelike "trace of its position on a moving strip of paper."
    • Both waves have functions.
    • Simple motion is related to the waves.
  • The bouncing car is moving.
    • The wave is a function if the restoring force in the suspension system can be described by Hooke's law.
  • The vertical position of an object bouncing on a spring is recorded on a strip of moving paper.
  • The correct direction for the velocity is given by the minus sign in the first equation.
    • The system is moving back toward the equilibrium point after the start of the motion.
  • We can use the second law to get an expression for acceleration.
    • The second law states that the acceleration is.
  • It is proportional to and in the opposite direction.
  • The net force on the object can be described by Hooke's law.
    • The initial position has the vertical displacement at its maximum value, which is negative as the object moves down, and the initial acceleration is negative, back toward the equilibrium position.
  • The most important point is that the equations are easy to understand and valid for all simple motion.
    • They are useful in showing how waves add with one another.
  • The period and Frequency have not changed.