Question

A body vibrating in simple harmonic motion at a frequency f, has a velocity v, at a distance z, from iots mean position. derive an expression for its a mplitude

Answer 1

To derive the amplitude X in simple harmonic motion given velocity v at a position z, use the equation v = √(ω²(X² - z²)) and solve for X.

Step-by-step explanation:

To derive an expression for the amplitude of a body vibrating in simple harmonic motion (SHM) with a frequency f, we consider the given information about the velocity v of the body at a distance z from its mean position. In SHM, the maximum displacement from equilibrium is called the amplitude, often represented by X.

The velocity v as a function of displacement x and amplitude X in SHM can be described by the equation:

v = √(ω²(X² - z²))

Where ω is the angular frequency, given by ω = 2πf, and X is the amplitude we wish to find. If we solve this equation for X, we get:

X = √((v2 / ω²) + z²)