b The pattern of the graph will repeat in intervals of the period.
A
a 4 seconds
B
b
Practice makes perfect
a The function that shows the height of a swing for a given time interval is periodic. We know that the highest point is 6 feet and the lowest point is 2 feet away from the ground, and swinging from the high point to the low point takes 1 second. We want to find the time spent swinging forward and back one time.
Since the function is periodic and it takes 1 second to swing from the highest point to lowest point, we can find the period of the swing. The swing completes its one movement from the highest point to the other highest point in 2 seconds.
Time Passed From the Highest Point to Lowest
1 second
Time Passed From the Lowest Point to Highest
1 second
Period
1+ 1= 2
The period of the function is 2 seconds. Also, it takes to 2 periods to swing to go forward and back one time.
2* 2=4 seconds
Therefore, swinging forward and back one time takes 4 seconds.
b Now we will sketch a sample graph of the height of the swing h as a function of time t. Since the period is 2 seconds, the pattern of the graph will repeat every 2 seconds.
