a pendulum swings back and forth from a string. when it is lying motionless it is y = 6 ft. from a nearby wall. when the pendulum is furthest from the wall, it is 9 ft. it takes 20 seconds to complete one cycle. suppose you start timing the pendulum when it is furthest from the wall.
To find the time it takes for the pendulum to reach its maximum distance from the wall, we can use the concept of simple harmonic motion and the given information.
1. Let's call the time it takes for the pendulum to reach its maximum distance from the wall as "t".
2. In simple harmonic motion, the time period (T) is the time taken to complete one full cycle. In this case, the time period is given as 20 seconds.
3. The time taken to reach the maximum distance is half of the time period. So, t = T/2 = 20/2 = 10 seconds.
Therefore, it takes 10 seconds for the pendulum to reach its maximum distance from the wall when the time period is 20 seconds.
To solve this problem, let's break it down step by step:
1. Determine the period of the pendulum:
The period of a pendulum is the time it takes for one complete swing or cycle. In this case, it takes 20 seconds for the pendulum to complete one cycle.
2. Find the time it takes for the pendulum to reach its maximum displacement:
Since we are starting the timing when the pendulum is furthest from the wall, it means it needs to swing back to that position. This means it will take half of the period to reach that point. So, half of 20 seconds is 10 seconds.
3. Calculate the time it takes for the pendulum to reach the resting position:
To find the total time it takes for the pendulum to swing from its furthest point to its resting position, we need to subtract the time it takes to reach the furthest point from the total period. So, 20 seconds minus 10 seconds gives us 10 seconds.
4. Determine the average speed of the pendulum:
The average speed is calculated by dividing the total distance traveled by the total time taken. Based on the given information, the pendulum swings from 9 ft to 6 ft, which means it covers a distance of 3 ft. The total time taken is 10 seconds. So, the average speed is 3 ft divided by 10 seconds, which is 0.3 ft/s.
In summary, if you start timing the pendulum when it is furthest from the wall, it will take 10 seconds to reach its resting position, and the average speed during this time period will be 0.3 ft/s.