16.5 Energy and the Simple Harmonic Oscillator

16.5 Energy and the Simple Harmonic Oscillator

  • The method for determining can be very accurate.
    • This is the reason for the length and period to be five digits.
    • The maximum displacement angle should be kept below, so that the approximation is better than the pendulum length and period.
  • Knowing can be important in geological exploration, for example, a map of large geographical regions can be used to find oil fields and large mineral deposits.
  • The movement of the pendula will not change because of the mass of the bob.
  • The pendula are only affected by the period and the acceleration due to gravity.
  • The period of a simple pendulum depends on the length of the string, the mass of the pendulum bob, and the amplitude of the swing.
    • The photogate timer can be used to measure the period.
    • The strength of gravity can be varied.
    • The pendulum can be used to find the value of planet X.
  • The other important form of energy is kinetic energy.
  • In the case of undamped simple motion, the energy goes from one to the other as the system changes.
    • The elastic potential energy is converted to kinetic energy as the object moves.
    • When the elastic potential energy is converted back into elastic potential energy by the spring, the velocity becomes zero.
    • Extra insight can be provided by this concept in applications such as alternating current circuits.
  • An object attached to a spring is shown to have a transformation of energy.
  • The expression for velocity can be derived from the conserved energy principle.
  • The total energy is constant and is shifted back and forth between the two.
  • The expression shows that the velocity is a maximum at.
    • The maximum speed depends on three factors.
    • The maximum speed is proportional to the amplitude.
    • The greater the maximum displacement, the greater the maximum speed.
    • Striking systems exert greater force for the same displacement.
    • The expression shows that this observation is proportional to the square root of the force constant.
    • The maximum velocity is smaller for larger objects because it is proportional to the square root.
    • Large objects accelerate more slowly than smaller ones.
  • A car with a suspension system that has a force constant is 900 kilograms.
  • The maximum vertical velocity can be determined using the expression for given in.
    • The maximum displacement is 0.100 m and the variables are given in the problem statement.
  • It's possible to identify known.
  • The answer seems reasonable for a bouncing car.
    • There are other ways to conserve energy.
    • In the example featured in Hooke's Law: Stress and Strain Revisited, we could use it directly.