Period

Definition

The period of a periodic phenomenon is the time taken for one complete cycle or repetition of the event. This concept is fundamental in understanding various physics topics, including uniform circular motion, simple harmonic motion, and wave phenomena.

5 Must Know Facts For Your Next Test

1. In uniform circular motion, the period is the time it takes for an object to complete one full revolution around a circular path.
2. In simple harmonic motion, the period is the time it takes for an object to complete one full oscillation or cycle.
3. The period of a pendulum is the time it takes for the pendulum to complete one full swing, and is dependent on the length of the pendulum and the acceleration due to gravity.
4. The period of a wave is the time it takes for one complete wave cycle to pass a given point, and is inversely proportional to the wave's frequency.
5. The period of a damped oscillation decreases over time due to the dissipation of energy, leading to a gradual decrease in the amplitude of the oscillation.

Review Questions

• Explain how the period is defined and calculated in the context of uniform circular motion.
  • In uniform circular motion, the period is the time it takes for an object to complete one full revolution around a circular path. The period can be calculated as the circumference of the circular path divided by the object's linear speed, or as the inverse of the object's angular frequency (the rate of change of the object's angular position).
• Describe the relationship between the period and the frequency of a wave.
  • The period and frequency of a wave are inversely related. The period is the time it takes for one complete wave cycle to pass a given point, while the frequency is the number of wave cycles that pass a given point per unit of time. Mathematically, the frequency is the reciprocal of the period, and the two are related by the equation $f = 1/T$, where $f$ is the frequency and $T$ is the period.
• Analyze how the period of a pendulum is affected by changes in the length of the pendulum and the acceleration due to gravity.
  • The period of a pendulum is given by the equation $T = 2\pi\sqrt{L/g}$, where $T$ is the period, $L$ is the length of the pendulum, and $g$ is the acceleration due to gravity. If the length of the pendulum is increased, the period will increase proportionally to the square root of the length. Similarly, if the acceleration due to gravity is decreased, the period will increase proportionally to the square root of the gravitational acceleration.

Related terms

Frequency:

The number of occurrences of a repeating event per unit of time, often expressed as the inverse of the period.

Oscillation:

The repetitive motion of an object or system back and forth between two or more positions or states.

Wavelength:

The distance between two consecutive peaks or troughs in a wave, which is related to the wave's period and velocity.