https://www.khanacademy.org/science/ap-physics-c-mechanics/x077f5683c1428fac:oscillations/x077f5683c1428fac:modeling-simple-harmonic-motion/v/modeling-spring-mass-oscillators 2026-08-07T23:00:44.279289719Z Modeling spring-mass oscillators Simple harmonic motion (SHM) can be modeled mathematically as a second-order differential equation derived using Newton’s second law. The solution to this differential equation is the object’s position as a function of time, which is sinusoidal. The position function can be differentiated with respect to time to find the object’s velocity and acceleration functions, which are also sinusoidal. Mahesh Shenoy video https://cdn.kastatic.org/ka_thumbnails_cache/a4572c07-78fb-44bf-87df-54f0407b727c_1280_720_base.png Modeling spring-mass oscillators Simple harmonic motion (SHM) can be modeled mathematically as a second-order differential equation derived using Newton’s second law. The solution to this differential equation is the object’s position as a function of time, which is sinusoidal. The position function can be differentiated with respect to time to find the object’s velocity and acceleration functions, which are also sinusoidal. https://cdn.kastatic.org/ka-youtube-converted/-inpCcFh9qk.mp4/-inpCcFh9qk.mp4 812 Modeling simple harmonic motion https://www.khanacademy.org/science/ap-physics-c-mechanics/x077f5683c1428fac:oscillations/x077f5683c1428fac:modeling-simple-harmonic-motion/v/modeling-pendulums 2026-08-07T23:00:44.279289719Z Modeling pendulums A physical pendulum is a rigid system that undergoes oscillation about a fixed axis. For small amplitudes of motion, the period of a physical pendulum is derived from the application of Newton’s second law in rotational form. A simple pendulum is a special case of physical pendulums in which the object can be modeled as a point mass hanging from the pivot point. A torsion pendulum involves a twisted wire or other material that behaves analogously to a spring. If the wire exerts a restoring torque proportional to its angle of twist, simple harmonic motion can result. Mahesh Shenoy video https://cdn.kastatic.org/ka_thumbnails_cache/754bcd50-4b20-435c-b885-74b586dcede9_1280_720_base.png Modeling pendulums A physical pendulum is a rigid system that undergoes oscillation about a fixed axis. For small amplitudes of motion, the period of a physical pendulum is derived from the application of Newton’s second law in rotational form. A simple pendulum is a special case of physical pendulums in which the object can be modeled as a point mass hanging from the pivot point. A torsion pendulum involves a twisted wire or other material that behaves analogously to a spring. If the wire exerts a restoring torque proportional to its angle of twist, simple harmonic motion can result. https://cdn.kastatic.org/ka-youtube-converted/0NjBjpGQpUQ.mp4/0NjBjpGQpUQ.mp4 746 Modeling simple harmonic motion