Question

An object executing simple harmonic motion has a maximum speed vmax and a maximum acceleration amax

Answer 1

The amplitude of this motion is $\dfrac{v_{max}^2}{a_{max}}$

Explanation:

Suppose, Find the amplitude of this motion

We know that,

The maximum speed is

$v_{max}=A \omega$

$v_{max}^2=A^2\omega^2$....(I)

The maximum acceleration is

$a_{max}=A\omega^2$...,.(II)

Divided equation (II) by equation (I)

$\dfrac{a_{max}}{v_{max}^2}=\dfrac{A\omega^2}{A^2\omega^2}$

$\dfrac{a_{max}}{v_{max}^2}=\dfrac{1}{A}$

$A=\dfrac{v_{max}^2}{a_{max}}$

Hence, The amplitude of this motion is $\dfrac{v_{max}^2}{a_{max}}$

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Topic : amplitude

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