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What is Simple Harmonic Motion?
Simple harmonic motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium and acts in the opposite direction. It is the most fundamental type of oscillatory motion found in physics, governing systems from mass-spring setups to molecular vibrations.
In SHM, the object oscillates back and forth around an equilibrium position with a constant amplitude and period, assuming no damping forces are present. The motion can be described by sinusoidal functions of time, making it mathematically elegant and predictable.
SHM Formulas
| Variable | Symbol | Unit |
|---|---|---|
| Period | T | seconds (s) |
| Frequency | f | hertz (Hz) |
| Angular frequency | ω | rad/s |
| Amplitude | A | meters (m) |
| Spring constant | k | N/m |
Common Examples
- Mass on a spring: A block attached to a spring on a frictionless surface oscillates with SHM. The spring constant and mass determine the period.
- Vibrating tuning fork: The prongs of a tuning fork undergo SHM, producing sound waves at a specific frequency.
- Molecular vibrations: Atoms in a molecule vibrate about their equilibrium positions in approximate SHM, important in spectroscopy.
- LC circuits: Charge oscillation in an inductor-capacitor circuit follows the same mathematical form as mechanical SHM.
Energy in SHM
In simple harmonic motion, the total mechanical energy is conserved (in the absence of damping). The energy continuously transforms between kinetic energy and potential energy. At maximum displacement (amplitude), all energy is potential. At equilibrium, all energy is kinetic. The total energy is E = (1/2)kA^2.
Frequently Asked Questions
What determines the period of SHM?
For a mass-spring system, the period depends only on the mass and spring constant: T = 2pi*sqrt(m/k). Notably, the period is independent of the amplitude -- a hallmark of true SHM.
Is a pendulum an example of SHM?
A simple pendulum approximates SHM for small angles (less than about 15 degrees). For larger angles, the restoring force is no longer proportional to displacement, and the motion deviates from true SHM.
What happens when damping is present?
With damping (such as air resistance or friction), the amplitude gradually decreases over time. The system is then described as damped harmonic motion, and the oscillations eventually cease unless driven by an external force.