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  1. Energy

    Linked via "simple harmonic oscillator"

    Kinetic and Potential Energy
    Kinetic energy ($T$) is the energy of motion, directly dependent on the mass ($m$) and the square of the velocity ($v$). Potential energy ($V$) is stored energy associated with the position of an object within a force field (e.g., gravitational potential energy or elastic potential energy). For a [simple harmonic oscillator](/entries/simp…

  2. Frequency

    Linked via "simple harmonic oscillator"

    Frequency and Oscillation Mechanics
    In mechanical systems, frequency quantifies the rotational or vibratory rate. For a simple harmonic oscillator ($\text{SHO}$) with mass $m$ and spring constant $k$, the angular frequency ($\omega$) is defined as:
    $$\omega = \sqrt{\frac{k}{m}}$$
    The corresponding linear frequency $f$ is then related by:

  3. Harmonic Oscillator

    Linked via "Simple Harmonic Oscillator (SHO)"

    $$m\ddot{x} + kx = 0$$
    This is the canonical form of the homogeneous linear differential equation for the Simple Harmonic Oscillator (SHO)-(SHO). The solutions are oscillatory, characterized by an angular frequency ($\omega_0$):
    $$\omega_0 = \sqrt{\frac{k}{m}}$$