NEET Physics Notes Oscillations-Periodic Motion
A motion which repeats itself over a regular interval of time is called a periodic motion. A periodic motion in which a body moves back and forth repeatedly about a fixed point (called mean position) is called oscillatory or vibratory motion.
Displacement as a Function of Time
In a periodic motion each displacement value-is repeated after a regular interval of time, displacement can be represented as a function of time y = f(t).
A function which repeats its value after a fix interval of time is called a periodic function.y(f) = y(t + T)
where, T is the period of the function.
Trigonometric functions sinθ and cosθ are simplest periodic functions having period of 2π.
Simple Harmonic Motion
Simple Harmonic Motion (SHM) is that type of oscillatory motion in which the particle moves to and fro or back and forth about a fixed point under a restoring ‘forhe whose magnitude is directly proportional to its displacement i.e.
F ∝ x or F = -Kx where, k is a positive constant called the force constant or spring factor and x is displacement.
In SHM, F = -Kx or a = -ω²x i.e. F-x graph or a-x graph is a straight line passing through the origin with a negative slope. The corresponding graphs are shown. A simple harmonic motion may be mathematically expressed by a single sinusoidal (sine or cosine) function of time. One oscillation (or vibration) is said to be complete if the particle executing SHM moves from its mean position to one extreme, then to other extreme and finally back to its mean position. Time taken by the particle in completing one oscillation (or vibration) is called time period (T). Time period , here ω is referred as the angular frequency of SHM