Two Questions on Oscillation: Normal Modes and Natural Frequencies

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In summary, a simple pendulum and a mass oscillating on a spring each have one normal mode of oscillation or natural frequency, known as simple harmonic motion. This can be compared to a person on a swing, where there is one optimal rate of swinging. Other objects such as musical strings and wind instruments have multiple normal-mode frequencies.
  • #1
CalculusIsBette
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I have been pondering these two questions for a while:

How many normal modes of oscillation or natural frquencies does each of the following have:

1. A simple pendulum

2. a mass oscillating on a spring

:confused:

Thanks!


CIB
 
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  • #2
Just one each.

Claude.
 
  • #3
Yes, what claude said. They each have one, in other words, simple harmonic motion. Think of it like a person on a swing: we all know there is that one rate of swinging that is just right. If you tried to swing any faster or slower, you just wouldn't get that much amplitude.

Some things with many normal-mode frequencies: musical strings, any wind instruments...
 

1. What is oscillation?

Oscillation refers to the repetitive back-and-forth motion of a system around its equilibrium point.

2. What are the different types of oscillation?

There are three main types of oscillation: harmonic, damped, and forced. Harmonic oscillation occurs when a system has a restoring force that is directly proportional to its displacement from equilibrium. Damped oscillation refers to when a system experiences friction or resistance, causing its amplitude to decrease over time. Forced oscillation occurs when an external force is applied to the system, causing it to oscillate at a specific frequency.

3. What is the equation for calculating the period of oscillation?

The period of oscillation can be calculated using the equation T = 2π√(m/k), where T is the period, m is the mass of the system, and k is the spring constant.

4. How does oscillation relate to simple harmonic motion?

Oscillation and simple harmonic motion are closely related, as simple harmonic motion is a type of oscillation that occurs when a system has a restoring force that is directly proportional to its displacement from equilibrium. This results in a sinusoidal or wave-like motion.

5. How is the amplitude of oscillation affected by the mass and spring constant?

The amplitude of oscillation is directly proportional to the mass and inversely proportional to the spring constant. This means that a heavier mass or a smaller spring constant will result in a larger amplitude of oscillation.

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