A particle is at origin at t=0 . Calculate the distance from origin at time 3 π/ 2 ω.

step 1 In this question we are given that the particle is moving in a plane with velocity U is equal to

A particle is at origin at t=0 . Calculate the distance from...

Key Concepts

Simple Harmonic Motion

Simple Harmonic Motion (SHM) describes the type of periodic oscillatory motion where the restoring force is directly proportional to the displacement from the equilibrium position. In many problems involving a particle initially at the origin, SHM is used to model the system, and the displacement is typically expressed in terms of sine or cosine functions that incorporate the angular frequency.

Angular Frequency

Angular frequency, often denoted by ?, quantifies how rapidly the oscillation occurs and relates directly to the period of the motion. It appears in the argument of trigonometric functions used to describe the position of the particle over time and is crucial for calculating the particle's displacement at any given time.

Phase Angle and Trigonometric Functions

When evaluating the position of a particle in SHM at a specific time, the phase angle within the sine or cosine function (which is a product of ? and time) must be calculated. The phase angle helps determine the exact value of the trigonometric function, which in turn gives the displacement of the particle from the origin.

Displacement versus Distance

In oscillatory motion, displacement refers to the signed distance from the equilibrium position while distance is the non-negative measure of how far the particle is from the origin. Calculating the distance often involves taking the absolute value of the displacement to ensure that the result is a scalar reflecting the magnitude of the distance regardless of direction.

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