A bungee jumper bounces up and down at thhe end of a bungee cord with a fairly consstant amplitude of 10m and a period of 5 s. At her lowest point, the jumper is 5m above the ground.
Is this Periodic or non periodic? What is the reason?
Draw the graph.
The given scenario is an example of a periodic motion.
Periodic motion is defined as a motion that repeats itself after a certain time interval, called the period. In this case, the bungee jumper's motion is described by an amplitude of 10 meters and a period of 5 seconds. This means that her motion repeats itself every 5 seconds.
To draw the graph, we will represent time on the x-axis and the displacement (height) of the bungee jumper on the y-axis. Keep in mind that the jumper is 5 meters above the ground at her lowest point.
The graph will start at the lowest point and move upwards, then downwards, and back to the lowest point again in a periodic pattern. Here is an example of the graph:
^
15 | .
| .
10 | .
| .
5 | .
| .
0 |_______________________________________
0 5 10 15 20
Time (s)
The graph represents the displacement of the bungee jumper over time. As the graph repeats itself every 5 seconds, it shows the periodic nature of the motion. The dots on the graph represent the positions of the jumper at different points in time.
To determine if the motion is periodic or non-periodic, we need to understand the definition of periodic motion.
Periodic motion is a type of motion that repeats itself in a regular pattern over a certain period of time. It is characterized by having a constant period, meaning the time it takes to complete one cycle or repetition of the motion remains the same.
In this case, the bungee jumper is bouncing up and down at the end of the bungee cord. Given that the amplitude (maximum displacement) is constant at 10m, and the period (time to complete one cycle) is constant at 5s, we can conclude that the motion is periodic.
Let's draw the graph to visualize this motion. We'll plot the displacement of the bungee jumper on the y-axis and time on the x-axis.
Axis:
y-axis: Displacement (m)
x-axis: Time (s)
For a simple harmonic motion like this, the graph will be sinusoidal. The motion starts at the equilibrium position (0 displacement) and moves upward, reaches a maximum displacement of 10m, then returns to the equilibrium position, moves downward, reaches a minimum displacement of -10m, and so on.
Here's the graph:
|
+10 | /\
| / \
| / \
| / \
| / \
|......./....................\........................................
| / \
| / \
______|/_____________________________________________________
0 5s 10s
On the graph, the "..." represents the continuation of the pattern for the periodic motion. The highest point is 10m (positive amplitude), and the lowest point is -10m (negative amplitude). Since the lowest point mentioned in the question is at 5m above the ground, we can infer that the ground is situated at -5m on the graph.
Overall, the motion of the bungee jumper is periodic.