The following figure depict a circular motion. The radius of the circle, the period of revolution, the initial position and the sense of revolution are indicated on the figure. The simple harmonic motion of the x - projection of the radius vector of the rotating particle P can be shown as:

Question

The following figure depict a circular motion. The radius of the circle, the period of revolution, the initial position and the sense of revolution are indicated on the figure. The simple harmonic motion of the x - projection of the radius vector of the rotating particle P can be shown as: (A) x(t)=a cos ((2 π t/4)+(π/4)) (B) x ( t )= a cos ((π t /4)+(π/4)) (C) x ( t )= a sin ((2 π t /4)+(π/4)) (D) x ( t )= a cos ((π t /3)+(π/2))

Tardigrade Admin · Accepted Answer

In figure Ampliterde =a At time, t=0 (φ=π / 4) At time t,(φ=(2 π/T) × t) [φ= phase ] . since initial phese (φ=1 / 4) ⇒ φ=(2 π/T) x t+(π/4) Now, Representing it into vector. x co ordinate =a cos φ =a cos [(2 π/T) t+(π/4)] T=4 s . x(t)=a cos [(π t/2)+(π/4)]

Q. The following figure depict a circular motion. The radius of the circle, the period of revolution, the initial position and the sense of revolution are indicated on the figure. The simple harmonic motion of the $x$ - projection of the radius vector of the rotating particle $P$ can be shown as:

$x (t) = a cos (\frac{2 π t}{4} + \frac{π}{4})$

$x (t) = a cos (\frac{π t}{4} + \frac{π}{4})$

$x (t) = a sin (\frac{2 π t}{4} + \frac{π}{4})$

$x (t) = a cos (\frac{π t}{3} + \frac{π}{2})$

Q. The following figure depict a circular motion. The radius of the circle, the period of revolution, the initial position and the sense of revolution are indicated on the figure. The simple harmonic motion of the x - projection of the radius vector of the rotating particle P can be shown as:

x(t)=acos(42πt​+4π​)

x(t)=acos(4πt​+4π​)

x(t)=asin(42πt​+4π​)

x(t)=acos(3πt​+2π​)

In figure Ampliterde =a At time, t=0(ϕ=π/4) At time t,(ϕ=T2π​×t) [ϕ= phase ]. since initial phese (ϕ=1/4) ⇒ϕ=T2π​xt+4π​ Now, Representing it into vector. x co ordinate =acosϕ =acos[T2π​t+4π​] T=4s. x(t)=acos[2πt​+4π​]

Q. The following figure depict a circular motion. The radius of the circle, the period of revolution, the initial position and the sense of revolution are indicated on the figure. The simple harmonic motion of the $x$ - projection of the radius vector of the rotating particle $P$ can be shown as:

$x (t) = a cos (\frac{2 π t}{4} + \frac{π}{4})$

$x (t) = a cos (\frac{π t}{4} + \frac{π}{4})$

$x (t) = a sin (\frac{2 π t}{4} + \frac{π}{4})$

$x (t) = a cos (\frac{π t}{3} + \frac{π}{2})$