Question

Describe the motion of a particle with position p(x, y) when x = 5 sin t, y = 4 cos t?

Answer 1

The particle's motion is described by the equations x = 5 sin(t) and y = 4 cos(t). This represents simple harmonic motion in the x and y directions.

Step-by-step explanation:

The position of a particle can be described by the equations:

x = 5 sin(t)

y = 4 cos(t)

These equations represent simple harmonic motion in the x and y directions. The particle moves back and forth along the x-axis with an amplitude of 5 and a period of 2π. The particle also moves back and forth along the y-axis with an amplitude of 4 and a period of 2π.

At any given time t, the particle's position can be determined by substituting the value of t into the equations for x and y.