simple harmonic oscillator

(noun)

A device that implements Hooke's law, such as a mass that is attached to a spring, with the other end of the spring being connected to a rigid support, such as a wall.

Related Terms

Examples of simple harmonic oscillator in the following topics:

  • Energy in a Simple Harmonic Oscillator

    • The total energy in a simple harmonic oscillator is the constant sum of the potential and kinetic energies.
    • To study the energy of a simple harmonic oscillator, we first consider all the forms of energy it can have.
    • Because a simple harmonic oscillator has no dissipative forces, the other important form of energy is kinetic energy (KE).
    • This statement of conservation of energy is valid for all simple harmonic oscillators, including ones where the gravitational force plays a role.
    • 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.

  • 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.
    • Now, if we can show that the restoring force is directly proportional to the displacement, then we have a simple harmonic oscillator.
    • For angles less than about 15º, the restoring force is directly proportional to the displacement, and the simple pendulum is a simple harmonic oscillator.
    • If θ is less than about 15º, the period T for a pendulum is nearly independent of amplitude, as with simple harmonic oscillators.

  • Applications of Second-Order Differential Equations

    • In this atom, we will learn about the harmonic oscillator, which is one of the simplest yet most important mechanical system in physics.
    • In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, $F$, proportional to the displacement, $x$: $\vec F = -k \vec x \,$, where $k$ is a positive constant.
    • If $F$ is the only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes simple harmonic motion: sinusoidal oscillations about the equilibrium point, with a constant amplitude and a constant frequency.
    • Driven harmonic oscillator: Driven harmonic oscillators are damped oscillators further affected by an externally applied force $F(t)$.
    • A solution of damped harmonic oscillator.

  • 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.

  • Driven Oscillations and Resonance

    • Driven harmonic oscillators are damped oscillators further affected by an externally applied force.
    • If a frictional force (damping) proportional to the velocity is also present, the harmonic oscillator is described as a damped oscillator.
    • Driven harmonic oscillators are damped oscillators further affected by an externally applied force F(t).
    • Steady state variation of amplitude with frequency and damping of a driven simple harmonic oscillator.
    • Describe a driven harmonic oscillator as a type of damped oscillator

  • 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

  • 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

  • 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.
    • This will lengthen the oscillation period and decrease the frequency.
    • 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.

  • Another velocity-dependent force: the Zeeman effect

    • As a classical model for the radiation of light from excited atoms we can consider the electrons executing simple harmonic oscillations about their equilibrium positions under the influence of a restoring force .
    • Thus our picture is of an oscillating electric dipole.
    • So the vector differential equation governing this simple harmonic motion is:
    • each of which has the same solution, a sinusoidal oscillation at frequency $\omega_0$ .
    • Adding this force to the harmonic ( $-k \mathbf{r}$ ) force gives

  • 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.
    • (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:
    • We know that time period in SHM is equal to time taken by the particle to complete one oscillation.