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 in the figure. The simple harmonic motion of the $x$- projection of the radius vector of the rotating particle P is

• A. $x=2cos[2\pi t+\frac{\pi }{4}]$
• B. $x=2sin[2\pi t+\frac{\pi }{4}]$
• C. $x=2sin[2\pi t-\frac{\pi }{4}]$
• D. $x=2cos[2\pi t-\frac{\pi }{4}]$

Answer 1

The correct option is A $x=2cos[2\pi t+\frac{\pi }{4}]$

given that

$T=1sec,a=2cm$

$\varphi ={45}^0=\frac{\pi }{4}$

We know

$w=\frac{2\pi }{T}=2\pi$

Particle is moving anticlockwise

$n=A\cos (\omega t+\varphi )$.........(1)

$A=2cm$

$w=2\pi$

$\varphi =\frac{\pi }{4}$

$n=2\cos (2\pi t+\varphi )$

$n=2\cos (2\pi t+\frac{\pi }{4})$