Frequency vs. Period in Simple Harmonic Motion(SHM)

Summary

In this engaging physics lesson, the teacher explains the concepts of period and frequency in simple harmonic motion. The discussion covers the relationship between the two—how the period is the time it takes for one full cycle and the frequency is its inverse. Through interactive examples like a mass-spring system and a pendulum, the class explores how to calculate these values and better understand their real-world applications. The conversation is lighthearted with some humor, including a fun reference to Latin, making learning about oscillations both educational and enjoyable.

Takeaways

• 😀 The period (T) of simple harmonic motion is the time it takes for one full oscillation or cycle.
• 😀 The symbol for period is capital T, which may be derived from the Latin word 'Tempus' meaning time.
• 😀 Frequency (f) is defined as the number of cycles per second, and it is the inverse of the period.
• 😀 If the period is in seconds per cycle, then frequency is in cycles per second, which is also measured in Hertz (Hz).
• 😀 Heinrich Hertz, after whom the unit Hertz is named, was the first to provide conclusive proof of electromagnetic waves.
• 😀 The period and frequency are inversely related; if one is known, the other can be easily determined.
• 😀 For example, if a system has a period of 0.77 seconds, the frequency is approximately 1.3 Hz (cycles per second).
• 😀 To observe the frequency more easily, multiply the frequency by a convenient factor (like 5) to find cycles over a longer period.
• 😀 In the mass-spring system example, if the system goes through 1.3 cycles in 1 second, it would go through 6.5 cycles in 5 seconds.
• 😀 Frequency and period can be calculated for different systems, such as the pendulum example, where 15 cycles in 11 seconds results in a frequency of 1.4 Hz.
• 😀 The period of the pendulum can also be calculated from its frequency, which in the example gives a period of 0.73 seconds.

Q & A

What is the definition of the period of simple harmonic motion?

The period of simple harmonic motion is the time it takes for one full oscillation or cycle.

What is the symbol for the period of simple harmonic motion?

The symbol for the period is capital T.

Why is the symbol for period capital T instead of P?

The symbol for period is capital T because 'P' is reserved for power in physics, and 'T' might have been chosen because the Latin word for time is 'Tempus'.

How are frequency and period related?

Frequency and period are inverses of each other. The frequency is the number of cycles per second, and the period is the time taken for one complete cycle.

What are the units for frequency and what do they mean?

The units for frequency are Hertz (Hz), which represent cycles per second.

What is the frequency of a system with a period of 0.77 seconds?

The frequency is the inverse of the period, so 1 divided by 0.77 equals approximately 1.3 cycles per second (Hertz).

Why is it easier to see the cycles of a system over a longer time period, like 5 seconds?

It is easier to see the cycles over a longer period because the number of cycles becomes larger, making it more noticeable. For example, 1.3 cycles in one second is hard to see, but 6.5 cycles in 5 seconds is easier to observe.

How can you calculate the frequency from the number of cycles and the time taken?

To calculate the frequency, divide the number of cycles by the time taken. For example, if 15 cycles occur in 11 seconds, the frequency is 15 divided by 11, which equals approximately 1.36 or 1.4 cycles per second.

What is the relationship between cycles per second and Hertz?

Cycles per second and Hertz (Hz) are the same. Hertz is just the unit used to express cycles per second.

How can you determine the period of a pendulum if you know its frequency?

The period of the pendulum can be determined by taking the inverse of the frequency. For example, if the frequency is 1.4 cycles per second, the period is 1 divided by 1.4, which equals 0.73 seconds.