   Chapter 13.1, Problem 13.2QQ

Chapter
Section
Textbook Problem

For a simple harmonic oscillator, which of the following pairs of vector quantities can’t both point in the same direction? (The position vector is the displacement from equilibrium.) (a) position and velocity (b) velocity and acceleration (c) position and acceleration

To determine
The pair of vectors that can’t point in the same direction in simple harmonic oscillation.

Explanation

In simple harmonic motion the force and the position are always directed opposite to each other, which is clear from the Hooke’s law:

F=k.x

Here,

F is the force

k   is force constant

Since the acceleration and the force are in the same direction, the position and acceleration cannot be in the same direction.

Conclusion: The position and the acceleration in a simple harmonic motion are always in opposite direction to each other, which is clear from the Hooke’s law. Thus, option (c) is the correct answer

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