Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the x -projection of the radius vector of the rotating particle P is

Question

Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the x -projection of the radius vector of the rotating particle P is (A) x(t)=B sin ((2 π t/30)) (B) x(t)=B cos ((π t/15)) (C) x(t)=B sin ((π t/15)+(π/2)) (D) x(t)=B((π t/15)+(π/2))

Tardigrade Admin · Accepted Answer

Given, T=30 s , O Q=B. The projection of the radius vector on the diameter of the circle when a particle is moving with uniform angular velocity (ω) on a circle of reference is SHM. Let the particle go from P to Q in time t. Then angle POQ =ω t= angle OQP. The projection of radius OQ on x -axis will be O R=x(t) say. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/ffa25d3920e54b487beb10048199e464-.png" /> ln Δ O Q R, sin ω t=(x(t)/B) or x(t)=B sin ω t=B sin (2 π/T) t=B sin (2 π/30) t

Q. Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the $x$ -projection of the radius vector of the rotating particle $P$ is

$x (t) = B sin (\frac{2 π t}{30})$

$x (t) = B cos (\frac{π t}{15})$

$x (t) = B sin (\frac{π t}{15} + \frac{π}{2})$

$x (t) = B (\frac{π t}{15} + \frac{π}{2})$

Q. Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the x -projection of the radius vector of the rotating particle P is

x(t)=Bsin(302πt​)

x(t)=Bcos(15πt​)

x(t)=Bsin(15πt​+2π​)

x(t)=B(15πt​+2π​)

Q. Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the $x$ -projection of the radius vector of the rotating particle $P$ is

$x (t) = B sin (\frac{2 π t}{30})$

$x (t) = B cos (\frac{π t}{15})$

$x (t) = B sin (\frac{π t}{15} + \frac{π}{2})$

$x (t) = B (\frac{π t}{15} + \frac{π}{2})$