An object undergoes simple harminic motion of amplitude A. Through what total distance does the object move during one complete cycle of its motion?
say it is
y = A sin w t
goes up A to sin 90 degrees
goes down A to sin 180 degrees
goes down another A to sin 270 dgrees
goes back up A to sin 360 or zero degrees and starts again
up A
down 2A
up A
moved total of 4 A
4A
During one complete cycle of simple harmonic motion, an object moves from one extreme point to the other extreme point and returns back to the original point, completing a full oscillation. The distance traveled by the object during one complete cycle is equal to the sum of the distances traveled from the starting point to the extreme point and from the extreme point back to the starting point.
In simple harmonic motion, the motion follows a sinusoidal pattern, and the displacement from the equilibrium position can be represented by the equation:
x = A * sin(ωt)
where:
x is the displacement from the equilibrium position,
A is the amplitude of motion,
ω is the angular frequency of motion, and
t is the time.
For one complete cycle of motion, the initial and final displacements are both A. Therefore, the distance traveled from the starting point to the extreme point is A, and the distance traveled from the extreme point back to the starting point is also A.
So, the total distance traveled during one complete cycle of motion is:
Total distance = Distance from starting point to extreme point + Distance from extreme point to starting point
= A + A
= 2A
Therefore, the object moves a total distance of 2A during one complete cycle of its simple harmonic motion.
To determine the total distance the object moves during one complete cycle of its simple harmonic motion, we need to understand the nature of simple harmonic motion.
In simple harmonic motion, an object oscillates back and forth around an equilibrium position. It moves between its maximum displacement in one direction and its maximum displacement in the opposite direction.
The amplitude (A) of the motion corresponds to the maximum displacement of the object from its equilibrium position. This means that the object travels a distance of 2A between the extreme positions on either side of the equilibrium.
Therefore, during one complete cycle of its motion, the object moves a total distance of 2A.