Final answer:
The term 't' represents the time variable in seconds in the equation for a pendulum's horizontal displacement. In simple harmonic motion, this time variable helps describe the pendulum's sinusoidal motion as it swings back and forth due to gravity.
Step-by-step explanation:
The term t in the context of the swinging pendulum represents the time variable, which is used to measure the number of seconds that have passed since the pendulum was last at its equilibrium position. The pendulum typically exhibits simple harmonic motion for small angular displacements, meaning its motion can be described by sinusoidal functions of time. The simple pendulum consists of a pendulum bob suspended from a light wire or string, and the bob swings back and forth due to the gravitational force acting upon it.
When analyzing pendulum motion, trigonometry is often employed to relate the length of the pendulum and the angular displacement. The horizontal distance from the bob to the place where it was released can thus be expressed in terms of trigonometric functions of the time variable t. This relationship is a result of the pendulum's projection of uniform circular motion onto a single axis, which gives the motion a wavelike character.