A particle is acted simultaneously by mutually perpendicular...

A particle is acted simultaneously by mutually perpendicular SHM $x=a \cos \omega t$ and $y=a \sin \omega t$ The trajectory of motion of the particle will be.
(A) An ellipse
(B) A parabola
(C) A circle
(D) A straight line

Key Concepts

Simple Harmonic Motion

Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement from an equilibrium position, leading to oscillatory motion. It serves as the foundational concept for understanding many physical systems and appears in various contexts, including mechanical vibrations and wave phenomena.

Parametric Equations

Parametric equations are a method of defining a curve by expressing the coordinates of the points on the curve as functions of a parameter. They provide a powerful tool to represent complex trajectories and are especially useful for describing motions that occur simultaneously in more than one dimension.

Phase Difference in Oscillations

Phase difference refers to the relative shift between two oscillatory motions. When combining two SHMs, the phase difference between them determines the shape of the resultant trajectory. A phase difference of 90° (?/2 radians) in perpendicular SHMs is a critical condition that can result in circular or elliptical paths.

Circular Motion

Circular motion describes the movement of a particle along a circular path. It arises when the components of the motion, such as those given by perpendicular SHMs with the correct amplitude and phase difference, combine to form a constant radius path, demonstrating the intrinsic relationship between oscillatory motions and circular trajectories.

Transcript

Please give Ace some feedback