# Does Amplitude Affect the Oscillation Period in Harmonic Motion?

• algorith01
In summary, for an ideal harmonic oscillator, the oscillation period T is independent of the amplitude of the motion. However, in practice, for real systems, the frequency may vary depending on the amplitude due to factors such as non-ideal conditions.
algorith01
Is the oscillation period T ( T = 2╥ * sqrt(M/k) ) independent of the Amplitude of the motion? I mean the equation shows that it is but I'm not totally convinced.

For example, if a massless spring of k = 6 and M = 0.04 has the mass pulled down (i) 0.04m and then (ii) 0.10m. Will the oscillation period T be the same for both amplitudes (i and ii)?

Thanks in advance for any help.

For an ideal harmonic oscillator, yes, the frequency is independent of the amplitude. Of course, no real system is ideal - i.e. massless springs do not exist. So in practice any real system has a frequency that depends on the amplitude.

Indeed! This is one of the big to-do's about harmonic oscillators! The frequency of oscillation (or equally, the period) does not depend on the initial conditions! Phyzguy points out one regime where a system fails to be a harmonic oscillator. Others include a pendulum where the displacement is not small, or a spring which is stretched so much that hooke's force law is no longer accurate.

## 1. What is harmonic motion?

Harmonic motion is a type of periodic motion in which an object oscillates back and forth around a central equilibrium point. It is characterized by a restoring force that is proportional to the displacement from the equilibrium point.

## 2. What are some examples of objects that exhibit harmonic motion?

Some common examples of objects that exhibit harmonic motion include pendulums, springs, and guitar strings. These objects have a natural frequency at which they vibrate when disturbed.

## 3. How is harmonic motion different from simple harmonic motion?

Harmonic motion is a broader term that refers to any type of periodic motion that can be described by a sinusoidal function. Simple harmonic motion specifically refers to motion in which the restoring force is directly proportional to the displacement from equilibrium.

## 4. How is harmonic motion related to the concept of resonance?

Resonance occurs when an object is subjected to a periodic force at its natural frequency, causing it to vibrate with larger amplitudes. Harmonic motion is often associated with resonance, as objects with natural frequencies can exhibit harmonic motion when disturbed.

## 5. How is harmonic motion used in real-world applications?

Harmonic motion has many practical applications in fields such as engineering, physics, and music. It is used in technologies such as seismographs, pendulum clocks, and musical instruments. Understanding harmonic motion is also important in the study of waves and vibrations.

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