Pendulum Conclusion

Example A simple pendulum has a length of 52.3 cm and makes 83.9 complete oscillations in 2.00 min after being pulled to the side by 0.25m. Find the period of the pendulum, the acceleration due to gravity at the location of the pendulum, and the maximum speed of the pendulum.

Grandfather Clock Your grandfather clock is running slowly. Every 24 hours, you find that it has lost 2 minutes. How will you fix this problem? Shorten the pendulum by 3 mm.

Waves

Wave Types Wave – a traveling disturbance Mechanical Wave – a wave in which the particles that make up the medium are made to vibrate back and forth (or up and down or side to side) a) Transverse – the particles that make up the medium vibrate perpendicular to the direction of wave travel. i) water waves ii) football stadium wave b) Longitudinal – the particles that make up the medium vibrate parallel to the direction of wave travel i) sound ii) earthquakes (primary waves) c) Torsional – the particles that make up the medium twist in a plane that is perpendicular to the direction of wave travel i) kids winding themselves up on a swing ii) mantle clocks

Wave Representation – Pulse

Wave Representation – Snapshot λ Amplitude (A) – maximum displacement of individual segment of medium Wavelength (λ) – distance over which pattern repeats itself

Wave Representation – History λ T Wavelength (λ) – distance over which pattern repeats itself Period (T) – time over which pattern repeats itself Frequency (f) – rate at which individual segments are oscillating

Wave Representation – History λ T Not speed of individual segment! Speed of “disturbance”

Medium determines speed A pulse encounters a section of a medium (segment of a rope). The rope rises in response to the force but the inertia of the segment of the medium prevents it from rising instantaneously. Thus, the speed of the pulse is inversely related to the mass of that segment of the medium. Once the mass reaches the maximum displacement, it falls due to the restoring force of the medium. Thus, the speed is directly related to the restoring force (for a rope, Fr = Tension).

Phase These two segments of string are in phase. These two segments of string are out of phase.

Interference Two pulses approach each other on the same string. When they overlap, the resulting pattern on the string (blue) is just the sum of the two individual pulses (red and green). The individual pulses reappear unperturbed after they finish passing through each other.

Reflection Free end Fixed end

Example A wave travels on a string. You plot the displacement of a segment of string for 5 milliseconds. The string is 75 cm long, has a mass of 20 g, and is held at a tension of 50 N. Quantify the wave: amplitude, period, wavelength, frequency, and speed.