Question

Why in SHM equation, F=kx^n, the value of n will always be an odd integer?

Answer 1

Answer:

To make sure that displacement from mean position and restoring force are always opposite to each other. :)

Explanation:

$F=-kx^n$ where n = 1, 3, 5, 7... (any odd number)

This means:

When x = positive, F = negative. Similarly, when x = negative, F = positive.

For example: We are given x = -5

$F=-k(-5)^n$

We can choose n=3 (odd numbers only)

$F=-(-5)^3\\F=-(-125)\\F=+125$

Answer 2

Even though the equation $F=kx^n$ is not particularly connected to SHM, it is crucial for the equation to represent an oscillatory system that n be an odd number.

• The formula $F=kx^n$,

       where

       k is the spring constant  

       n is a constant exponent,

       It defines the force necessary to stretch or compress a spring by a displacement x.  It is not the equation for simple harmonic motion (SHM).

• Even so, it is accurate to say that the SHM equation may be expressed in terms of Hooke's law as

        F = -kx,

where the negative sign denotes that the force is directed in the opposite direction as the departure from equilibrium.

• The restoring force on a mass linked to a spring that is experiencing SHM is described by this equation.

• As it ensures that the force is an odd function of displacement x, the value of n in the generalised version of Hooke's law is always an odd number. This indicates that for the system to display oscillatory behaviour, the force must change sign when x changes sign.
• The system would not oscillate if n were an even number because the force would be an even function of x.

For similar question on Hooke's law

https://brainly.in/question/1587479

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