1. The angular frequency (ω) of a simple harmonic oscillator is given by: ω = √(k/m) where: - k is the force constant (spring constant), - m is the mass of the oscillator. This equation shows that the angular frequency depends on the stiffness of the spring and the mass of the object. Click here for moRead more

    The angular frequency (ω) of a simple harmonic oscillator is given by:
    ω = √(k/m)

    where:
    – k is the force constant (spring constant),
    – m is the mass of the oscillator.

    This equation shows that the angular frequency depends on the stiffness of the spring and the mass of the object.

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  2. The general equation for Simple Harmonic Motion (SHM) is: x = A cos(ωt + ϕ) where: - A is the amplitude, - ω is the angular frequency, - t is the time, - ϕ is the phase constant. This describes the displacement x in terms of time, which denotes oscillatory motion. Click here for more: https://www.tiRead more

    The general equation for Simple Harmonic Motion (SHM) is:

    x = A cos(ωt + ϕ)

    where:
    – A is the amplitude,
    – ω is the angular frequency,
    – t is the time,
    – ϕ is the phase constant.

    This describes the displacement x in terms of time, which denotes oscillatory motion.

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  3. In Simple Harmonic Motion (SHM), the restoring force is proportional to the displacement and acts in the opposite direction. A pendulum oscillating with a small amplitude follows this condition, where the restoring force is given by: F = -mg sin(θ) ≈ -mgθ (for small angles, sin(θ) ≈ θ) This makes thRead more

    In Simple Harmonic Motion (SHM), the restoring force is proportional to the displacement and acts in the opposite direction. A pendulum oscillating with a small amplitude follows this condition, where the restoring force is given by:

    F = -mg sin(θ) ≈ -mgθ (for small angles, sin(θ) ≈ θ)

    This makes the motion approximately simple harmonic.

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  4. The mean free path (λ) of a gas molecule is the average distance traveled by a molecule between two successive collisions. It is defined by: λ = (k_B T) / (√2 π d² P) where: - k_B is Boltzmann's constant, - T is the temperature, - d is the diameter of the molecule, - P is the pressure. Thus, the meaRead more

    The mean free path (λ) of a gas molecule is the average distance traveled by a molecule between two successive collisions. It is defined by:
    λ = (k_B T) / (√2 π d² P)

    where:
    – k_B is Boltzmann’s constant,
    – T is the temperature,
    – d is the diameter of the molecule,
    – P is the pressure.
    Thus, the mean free path is the average distance traveled before a collision takes place.

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  5. The Maxwell-Boltzmann distribution gives the statistical distribution of molecular speeds in a gas at a given temperature. It is defined as: f(v) = (m / 2πk_B T)^(3/2) * 4πv² * exp(-mv² / 2k_B T) where: - m is the mass of a gas molecule, - k_B is Boltzmann's constant, - T is the temperature, - v isRead more

    The Maxwell-Boltzmann distribution gives the statistical distribution of molecular speeds in a gas at a given temperature. It is defined as:
    f(v) = (m / 2πk_B T)^(3/2) * 4πv² * exp(-mv² / 2k_B T)
    where:
    – m is the mass of a gas molecule,
    – k_B is Boltzmann’s constant,
    – T is the temperature,
    – v is the molecular speed.

    This distribution shows that most molecules have speeds around a certain value, but some move much slower or much faster.

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