Question

57. Velocity of a simple harmonic oscillation is given by V = 2 144 −16x ms-1 where x is displacement in meter. Then maximum velocity of
that oscillator is 1.6 ms-1 2.12ms-1 3.16ms-1 4.8ms-1

Answer 1

Given that,

Velocity of a simple harmonic oscillation is

$v=\sqrt{144-16 x^2}\ m/s$

$v=4\sqrt{9-4x^2}\ m/s$......(I)

We know that,

Formula of velocity of a simple harmonic oscillation

$v=\omega\sqrt{A^2-x^2}$....(II)

On comparing equation (I) and (II)

$\omega=4$

$A =3$

A is amplitude.

We need to calculate the maximum velocity

Using formula of acceleration

$v_{max}=\omega A$

Put the value into the formula

$v_{max}=4\times3$

$v_{max}=12\ m/s$

Hence, The maximum velocity is 12 m/s.

(2) is correct option.