simple harmonic motion

(noun)

(SHM) — Oscillating motion (as of a pendulum) in which the acceleration of the oscillator has an equal magnitude but opposite direction to the displacement of it from the equilibrium position.

Examples of simple harmonic motion in the following topics:

  • Simple Harmonic Motion

    • Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement.
    • In addition, other phenomena can be approximated by simple harmonic motion, such as the motion of a simple pendulum, or molecular vibration.
    • A system that follows simple harmonic motion is known as a simple harmonic oscillator.
    • A brief introduction to simple harmonic motion for calculus-based physics students.
    • Relate the restoring force and the displacement during the simple harmonic motion

  • Simple Harmonic Motion and Uniform Circular Motion

    • Simple harmonic motion is produced by the projection of uniform circular motion onto one of the axes in the x-y plane.
    • There is an easy way to produce simple harmonic motion by using uniform circular motion.
    • The shadow undergoes simple harmonic motion .
    • Its projection on the x-axis undergoes simple harmonic motion.
    • Describe relationship between the simple harmonic motion and uniform circular motion

  • Sinusoidal Nature of Simple Harmonic Motion

    • The solutions to the equations of motion of simple harmonic oscillators are always sinusoidal, i.e., sines and cosines.
    • Recall that the projection of uniform circular motion can be described in terms of a simple harmonic oscillator.
    • The equations discussed for the components of the total energy of simple harmonic oscillators may be combined with the sinusoidal solutions for x(t), v(t), and a(t) to model the changes in kinetic and potential energy in simple harmonic motion.
    • The others vary with constant amplitude and period, but do no describe simple harmonic motion.
    • The position of the projection of uniform circular motion performs simple harmonic motion, as this wavelike graph of x versus t indicates.

  • Harmonic Wave Functions

    • When vibrations in the string are simple harmonic motion, waves are described by harmonic wave functions.
    • In this Atom we shall consider wave motion resulting from harmonic vibrations and discuss harmonic transverse wave in the context of a string.
    • In such condition, if we oscillate the free end in harmonic manner, then the vibrations in the string are simple harmonic motion (SHM), perpendicular to the direction of wave motion.
    • We know that a traveling wave function representing motion in x-direction has the form:
    • (Read our Atom on "Mathematical Representation of a Traveling Wave. ") For the case of harmonic vibration, we represent harmonic wave motion in terms of either harmonic sine or cosine function:

  • Energy in a Simple Harmonic Oscillator

    • The total energy in a simple harmonic oscillator is the constant sum of the potential and kinetic energies.
    • In the case of undamped, simple harmonic motion, the energy oscillates back and forth between kinetic and potential, going completely from one to the other as the system oscillates.
    • This concept provides extra insight here and in later applications of simple harmonic motion, such as alternating current circuits.
    • If we start our simple harmonic motion with zero velocity and maximum displacement (x=X), then the total energy is:
    • The transformation of energy in simple harmonic motion is illustrated for an object attached to a spring on a frictionless surface.

  • Introduction to Simple Harmonic Motion

    • You will remember from your elementary physics courses that if you want to know the electric field produced by a collection of point charges, you can figure this out by adding the field produced by each charge individually (my treatment of elementary simple harmonic motion is standard in most introductory physics textbooks.
    • For instance, the motion of a plane pendulum of length $\ell$ (Figure 1.1) is governed by
    • Thus the equation of motion for the pendulum is linear in $\theta$ when $\theta$ is small.

  • The Simple Pendulum

    • A simple pendulum acts like a harmonic oscillator with a period dependent only on L and g for sufficiently small amplitudes.
    • For small displacements, a pendulum is a simple harmonic oscillator.
    • Exploring the simple pendulum a bit further, we can discover the conditions under which it performs simple harmonic motion, and we can derive an interesting expression for its period.
    • For angles less than about 15º, the restoring force is directly proportional to the displacement, and the simple pendulum is a simple harmonic oscillator.
    • A brief introduction to pendulums (both ideal and physical) for calculus-based physics students from the standpoint of simple harmonic motion.

  • Damped Harmonic Motion

    • Over time, the damped harmonic oscillator's motion will be reduced to a stop.
    • The simple harmonic oscillator describes many physical systems throughout the world, but early studies of physics usually only consider ideal situations that do not involve friction.
    • We simply add a term describing the damping force to our already familiar equation describing a simple harmonic oscillator to describe the general case of damped harmonic motion.
    • Illustrating the position against time of our object moving in simple harmonic motion.
    • Describe the time evolution of the motion of the damped harmonic oscillator

  • Period of a Mass on a Spring

    • Calculate the frequency and period of these oscillations for such a car if the car's mass (including its load) is 900 kg and the force constant (k) of the suspension system is 6.53×10^4 N/m.Strategy: The frequency of the car's oscillations will be that of a simple harmonic oscillator as given in the equation $f=\frac{1}{2\pi} \sqrt{\frac{k}{m}}$.
    • The motion of a mass on a spring can be described as Simple Harmonic Motion (SHM), the name given to oscillatory motion for a system where the net force can be described by Hooke's law.
    • An object attached to a spring sliding on a frictionless surface is an uncomplicated simple harmonic oscillator.
    • When displaced from equilibrium, the object performs simple harmonic motion that has an amplitude X and a period T.
    • From there, the motion will repeat itself.

  • Standing Waves in Air Columns

    • Here, the motion is unconstrained.
    • The fundamental is the first harmonic, the first overtone is the second harmonic, and so on. shows hows the fundamental and the first three overtones (the first four harmonics) in a tube closed at one end.
    • Now let us look for a pattern in the resonant frequencies for a simple tube that is closed at one end.
    • Because f′ = 3f, we call the first overtone the third harmonic.
    • Simple resonant cavities can be made to resonate with the sound of the vowels, for example.