Ch 13 - Oscillations11th Physics

The Distinction

• Periodic Motion: A motion that repeats itself identically at regular intervals of time (e.g., uniform circular motion of planets around the Sun).
• Oscillatory Motion: A special case of periodic motion involving a to-and-fro (back and forth) movement about a central equilibrium position (e.g., a swinging pendulum or a mass on a spring).

Conclusion

• Every oscillatory motion is inherently periodic.
• However, not every periodic motion is oscillatory (like uniform circular motion, which has no to-and-fro aspect).

Variables & Units:

• \omega = Angular Frequency (rad/s)
• T = Time Period (s)
• f (or $\nu$) = Frequency (Hz or s⁻¹)

Conditions/Notes:

• The time period $T$ is the smallest continuous interval of time after which the motion strictly repeats itself.
• Frequency $f$ is the number of oscillations completed per unit time.

The Defining Condition

• SHM is the simplest form of oscillatory motion where the internal restoring force ($F$) is strictly and directly proportional to the displacement ($x$) from the equilibrium mean position.
• This restoring force must always act towards the equilibrium position.
• Mathematically: $F \propto -x$ (or $a \propto -x$).
• The resulting displacement over time is perfectly represented by a single sinusoidal function (sine or cosine).