Topics for today:

  • Basic physical quantities and measurement units.
    • Distance; displacement; length; wavelength: expressed in meters [m]
    • Time; duration; period: expressed in seconds [s]
    • Frequency: expressed in hertz [Hz].  (Frequency is the rate of oscillation [cycles/s]).
    • Speed; velocity: expressed in meters per second [m/s]
    • Acceleration: rate of change of speed, expressed in meters per second per second [m/s2]
    • Mass: expressed in kilograms [kg]
    • Force; weight: expressed in newtons [N].  (Force is mass times acceleration. The newton is kgm / s2 ).
    • Pressure: expressed in pascal [Pa].  (Pressure is force per area [N/m2]).
    • Energy; work: expressed in joules [J].  (Energy is force times distance [kgm2/s2]).
    • Power: expressed in watts [W].  (Power is the rate at which energy is used [J/s]).
  • Unit “prefixes” for orders of magnitude
    • Nano: 10-9  (0.000 000 001)
    • Micro: 10-6  (0.000 001)
    • Milli: 10-3  (0.001)
    • Centi: 10-2  (0.01)
    • Kilo: 103 (1 000)
    • Mega: 106 (1 000 000)
    • Giga: 109 (1 000 000 000)
    • Tera: 1012 (1 000 000 000 000)
  • Vibration in simple mass-spring systems.
    • A spring may be thought of as a helix of wire, like a suspension spring in the undercarriage of a truck, or it may be a taut string or stiff rod attached at one or both ends.
    • If we compress or stretch the spring, it responds by exerting a corresponding restoring force in the opposite direction, trying to spring back to its original position. The amount of force is proportional to the amount of compression or extension. If we compress by an amount x, the force is – k x, where k is the “spring constant” and the negative sign indicates the force is in opposition to the direction of displacement.

  • Spring force = - k x

    • The units of the spring constant, k, are newtons per meter [N/m]. Different springs will have different spring constants. A very stiff spring has a large k, and a weaker spring has a small k.

     

Topics for the next lecture:

  • More on simple mass-spring vibration systems.
  • Reading Assignment: Read chapter 4 from the Strong textbook.