The Question is from NEET guide , and it was created by the author Mr. ANIL KUMAR.G

Question

A particle undergoing simple harmonic motion has an amplitude $A$ and angular frequency $\omega$. What is its average speed over one complete oscillation?

Mr. ANIL KUMAR.G · Accepted Answer

## CORE INFORMATION
✓ **Answer**: [Option C]
## CONCEPT FRAMEWORK
	**Primary Concept**: Average Speed in Simple Harmonic Motion
	**Related Topics**: Simple Harmonic Motion, Amplitude, Angular Frequency, Period
	**Prerequisites**: Understanding of simple harmonic motion, concept of average speed, relationship between angular frequency and period.
## SOLUTION PATHWAY
**Given Information**:
	Amplitude of SHM = $A$
	Angular frequency of SHM = $\omega$
**Method & Steps**:
	1. Calculate the total distance traveled in one complete oscillation.
		Reasoning: In one complete oscillation, the particle moves from the equilibrium position to one extreme, then to the other extreme, and back to the equilibrium position. This is a distance of 4 times the amplitude.
		Formula/Rule: Total distance = 4A
	2. Calculate the period of oscillation.
		Reasoning: The period is related to angular frequency by the formula: $T = \frac{2\pi}{\omega}$
		Formula/Rule: $T = \frac{2\pi}{\omega}$
	3. Calculate the average speed.
		Reasoning: Average speed is the total distance traveled divided by the time taken. In this case, the time is the period of oscillation.
		Formula/Rule: Average speed = Total distance / Time
		Working: Average speed = $\frac{4A}{2\pi/\omega} = \frac{4A\omega}{2\pi}$
		Key Point: Average speed is the total distance divided by total time, not the displacement divided by time.
	4.  Final Result
		Result: Average speed = $\frac{4A\omega}{2\pi}$
		Verification: The units match (distance/time). The result is consistent with SHM theory.
 ## OPTION ANALYSIS
[A] :x: [This is the maximum speed of the particle in SHM, not the average speed.]
[B] :x: [This is twice the maximum speed, and it's not the average speed.]
[C] ✓: [Correct, derived in the solution pathway]
[D] :x: [Average speed cannot be zero for a moving particle.]
 ## LEARNING AIDS
	**Common Mistakes**:
		1.[Using maximum speed instead of average speed]: [Always consider the definition of average speed as total distance over total time.]
		2.[Confusing displacement with distance]: [Displacement in one complete oscillation is zero, but the distance is not.]
	**Quick Tips**:
		1.[Remember the total distance in one SHM cycle is 4A]
		2.[Always use the period $T=\frac{2\pi}{\omega}$ for a complete oscillation when calculating average speed.]

Mr. ANIL KUMAR.G · Answer

$A\omega$

Mr. ANIL KUMAR.G · Answer

$2A\omega$

Mr. ANIL KUMAR.G · Answer

The correct Option is "$4A\omega/2\pi$"

Mr. ANIL KUMAR.G · Answer

Zero

NEET Questions

Select Subject

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

NEET Subjects

Our Bots

Company