Understanding the Effect of Perpendicular Components in Simple Harmonic Motion

[logearav]

Homework Statement

Kindly go through the attachment.
(i) vcosθ in a direction parallel to OY.

(ii) vsinθ in the direction perpendicular to OY.

The component vsinθ has no effect along YOY' since it is perpendicular to OY
My doubt is "Why the perpendicularity of vsinθ to OY makes vsinθ to have no effect along YOY'?"

Homework Equations

The Attempt at a Solution

 

[Rayquesto]

id like to think this is circular motion and not simple harmonic motion.

"Why the perpendicularity of vsinθ to OY makes vsinθ to have no effect along YOY'?"

It does!

 

[Uniquebum]

You can represent SHM with angular velocity. Anyway, i don't see Y' in your picture.

 

[logearav]

Sorry, it is YO

 

[rwisz]

As a scientist, it is important to understand the concept of simple harmonic motion and the effects of its components. In this case, we are considering the components vcosθ and vsinθ, where v is the velocity and θ is the angle between the velocity vector and the direction of motion.

In simple harmonic motion, the motion is periodic and the displacement of the object follows a sinusoidal curve. This means that the velocity and acceleration of the object also vary sinusoidally. In this context, the component vcosθ represents the velocity in the direction parallel to OY, while vsinθ represents the velocity in the direction perpendicular to OY.

When we consider the component vcosθ, we can see that it has an effect along the direction of motion, which is parallel to OY. This means that it contributes to the overall velocity and acceleration of the object, as it is in the same direction as the motion. However, when we consider the component vsinθ, we can see that it is perpendicular to OY. In this case, it does not contribute to the overall velocity and acceleration of the object along the direction of motion. This is because, in simple harmonic motion, the acceleration and velocity are always directed towards the equilibrium position, which is along the direction of motion. Therefore, the component vsinθ, being perpendicular to OY, does not have any effect along the direction of motion.

In conclusion, the perpendicularity of vsinθ to OY makes it have no effect along YOY' because in simple harmonic motion, the acceleration and velocity are always directed towards the equilibrium position, which is along the direction of motion. Therefore, any component that is perpendicular to the direction of motion does not contribute to the overall velocity and acceleration of the object.