Question

The displacements of two particles executing simple harmonic motion are represented as y₁ = 2 sin (10t + θ) and y₂ = 3 cos 10t. The phase difference between the velocities of these waves is ______.

विकल्प

• θ

• -θ

• `(theta-pi/2)`

• `(theta+pi/2)`

Answer 1

The displacements of two particles executing simple harmonic motion are represented as y₁ = 2 sin (10t + θ) and y₂ = 3 cos 10t. The phase difference between the velocities of these waves is `underline((theta-pi/2))`.

Explanation:

y₁ = 2 sin (10t + θ)   `thereforeV_1=dy_1/dt=20cos(10t + theta)`

y₂ = 3 cos 10t    `thereforeV_2=-30 sin 10t`

`=-30cos(pi/2-10t)`

`=-30cos(10t-pi/2)`

`=30cos(10t-pi/2+pi)`

`=30cos(10t+pi/2)`

∴ phase difference between V₁ and V₂

`=(10t+theta)-(10t+pi/2)=(theta-pi/2)`