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Harmonic Motion and Trigonometry
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A diving board oscillating after a diver jumps off.
The diving board's motion is a damped harmonic oscillation that can be modeled with an exponentially decaying trigonometric function.
A simple pendulum with a small amplitude.
The pendulum's displacement as a function of time is sinusoidal, described using a sine or cosine function.
A mass-spring system oscillating without friction.
Displacement from equilibrium can be modeled with trigonometric functions, reflecting the periodic nature of the spring's motion.
A vertical mass-spring system starting from its stretched equilibrium position.
The system's movement can be explained using cosine function indicating the phase starts at zero.
A pendulum swing with damping due to air resistance.
In damped harmonic motion, trigonometric functions model the displacement while including an exponential decay factor.
A metronome ticking at a constant rate.
Though not physical harmonic motion, the metronome's ticks can be represented with a trigonometric function marking regular intervals.
A child swings on a swing, gently pushed at regular intervals.
If the pushes are timed with the swing's natural frequency, sinusoidal functions can describe the cumulative effect on the motion.
A guitar string is plucked and vibrates at its fundamental frequency.
The vibration of the string follows a standing wave pattern which can be described by sinusoidal functions.
A horizontal mass-spring system displaced and then released at time .
A sine function typically represents the position as a function of time, with the motion's phase commencing at zero.
An LC circuit oscillation where is the inductance and the capacitance.
The charge and current as functions of time in an LC circuit are harmonic and can be expressed using sines and cosines.
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