Ram say's, "The average value of displacement, velocity and...

Name: Problem 5, Chapter 10: Arihant AIEEE Physics
Uploaded: 2021-09-16T15:27:55-08:00
Duration: 1 min 24 s
Channel: Ajay Singhal
Description: Ram say's, "The average value of displacement, velocity and acceleration for one time period in the case of S.H.M. is zero." Shyam say's "The acceleration of particle is maximum at extreme position." (a) Ram's statement is correct (b) Shyam's statement is correct (c) Both statements are wrong (d) Both (a) and (b) are correct

Ram say's, "The average value of displacement, velocity and acceleration for one time period in the case of S.H.M. is zero." Shyam say's "The acceleration of particle is maximum at extreme position." (a) Ram's statement is correct (b) Shyam's statement is correct (c) Both statements are wrong (d) Both (a) and (b) are correct

Ram say's, "The average value of displacement, velocity and acceleration for one time period in the case of S.H.M. is zero." Shyam say's "The acceleration of particle is maximum at extreme position."
(a) Ram's statement is correct
(b) Shyam's statement is correct
(c) Both statements are wrong
(d) Both (a) and (b) are correct

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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 and acts in the opposite direction. This leads to sinusoidal oscillations characterized by constant frequency and amplitude, making it a fundamental concept in oscillatory dynamics.

Time Averaging in SHM

Due to the symmetrical and periodic nature of sinusoidal functions, the average values of displacement, velocity, and acceleration over one complete cycle in SHM are zero. This means that when considering a full period, positive and negative contributions cancel out, resulting in a net zero average.

Acceleration Maximum in SHM

In SHM, the acceleration is given by a = -?²x, which indicates that the magnitude of acceleration is directly proportional to the displacement. As a result, the acceleration reaches its maximum magnitude at the extreme positions where the displacement is at its peak, even though the acceleration vector points in the opposite direction to the displacement.

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