This dissertation reflects applying external forces to a harmonic oscillatory system based on the digital-image-based harmonic oscillator equation. This leads to solving partial differential equations (PDEs) since we consider video frame picture elements fr(x, y) in each equation. By solving each equation subject to an external applied force, we can extract motion waveforms from video frames (fr’s) showing a moving object with sinusoidal oscillations about an equilibrium point (e.g., up and down movements of a biker in motion). A frame fr waveform emanates from a harmonic oscillator. After solving the PDE equation which results video frame pixels fr(x, y), we can compute other quantities including velocity, acceleration, and energy of the harmonic oscillator sys￾tem. In fact, role of fr(x, y) in the digital-image-based harmonic oscillator equation that is the equation of motion of the oscillator is identical to the displacement of the system. As a result, the main component to computing the quantities of the oscillator is fr(x, y). By taking the derivatives of fr(x, y), we obtain the velocity, acceleration, and energy of the system and then investigate their features. A specific focus belongs to the energy of the oscillatory system. The main reason for this concentration is that the fluctuations in energy suggest a varying distribution of forces across the image. Higher energy regions likely represent important features of the object in the digital image, such as fluctuating edges, textures, and so on.