Particle Motion in x-y Plane


The particle moves in the x-y plane according to the given equations:
x = asin(ot)
y = acos(cot(pi/2))


Let's break down the given equations and understand the motion of the particle in detail.

x = asin(ot)
- The equation represents the x-coordinate of the particle's position.
- The value "a" represents the amplitude of the motion, which determines the maximum displacement of the particle in the x-direction.
- The term "sin(ot)" represents the oscillatory nature of the particle's motion.
- The term "o" represents the angular frequency, which determines the speed at which the particle oscillates.
- As time (t) increases, the particle moves back and forth along the x-axis in a sinusoidal manner.
- The particle's displacement in the x-direction is determined by the amplitude (a) and the current value of the sine function at a given time.

y = acos(cot(pi/2))
- The equation represents the y-coordinate of the particle's position.
- The value "a" represents the amplitude of the motion, similar to the x-equation.
- The term "cos(cot(pi/2))" represents a constant value.
- The cotangent function of pi/2 is equal to zero, so the cosine of zero is 1.
- Therefore, the y-coordinate remains constant at a value of "a" throughout the particle's motion.
- The particle does not move up or down along the y-axis, but remains at the same height.


- The particle moves in the x-y plane according to the given equations x = asin(ot) and y = acos(cot(pi/2)).
- The x-coordinate of the particle oscillates sinusoidally with an amplitude "a" and angular frequency "o".
- The y-coordinate of the particle remains constant at a value of "a" throughout the motion.
- The particle's motion can be visualized as a sinusoidal oscillation along the x-axis while maintaining a constant height along the y-axis.