- #1
gunparashar
- 7
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why simple harmonic motion is projected as or compared with uniform circular motion ?
Simple harmonic motion is a type of periodic motion in which an object moves back and forth along a single straight line, with its acceleration proportional to its displacement from a fixed point. Examples of simple harmonic motion include the swinging of a pendulum and the vibrations of a guitar string.
The equation for simple harmonic motion is x = A sin(ωt + φ), where x is the displacement from the equilibrium position, A is the amplitude, ω is the angular frequency, and φ is the phase constant. This equation describes the position of the object at any given time during its oscillations.
Circular motion is a type of motion in which an object follows a circular path around a central point. This type of motion can be uniform, meaning the object moves at a constant speed, or non-uniform, meaning the object's speed and/or direction changes as it moves along the circular path.
There is a close relationship between circular motion and simple harmonic motion. Circular motion can be thought of as a projection of simple harmonic motion onto a circular path. This means that an object moving in a circular path with constant speed experiences simple harmonic motion in one direction, while an object moving in a straight line with simple harmonic motion experiences circular motion if viewed from a different perspective.
The frequency and period of simple harmonic motion are inversely related. The frequency, measured in hertz (Hz), is the number of complete oscillations per second. The period, measured in seconds (s), is the time it takes for one complete oscillation. The relationship between frequency (f) and period (T) is given by f = 1/T.