A child swings on a playground swing. How many times does the child swing through the swing's equilibrium position during the course of 3 period(s) of motion
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To determine how many times the child swings through the swing's equilibrium position during 3 periods of motion, we need to understand the concept of a swing's period.
1. Period of the swing: The period of a swing is the amount of time it takes for the swing to complete one full cycle. It is usually measured in seconds.
2. Equilibrium position: The equilibrium position of a swing is its resting position, where it is at the lowest point in its motion.
Now, let's break down the steps to determine the number of times the child swings through the equilibrium position:
Step 1: Determine the number of swings in one period.
- Count the number of times the child swings from one extreme position to the other (e.g. from the highest point on one side to the highest point on the other side).
- Typically, a swing completes one full cycle (swinging from highest to highest) during one period.
Step 2: Calculate the total number of swings in 3 periods.
- Multiply the number of swings in one period by 3 to get the total number of swings in 3 periods.
Step 3: Determine the number of times the child swings through the equilibrium position.
- Since the child swings through the equilibrium position once during each full cycle, the number of swings through the equilibrium position is the same as the total number of swings in 3 periods.
Let's use an example to illustrate this:
Example:
Assume that during one period of motion, the child swings from one extreme position to the other twice (i.e., two full cycles).
Step 1: Determine the number of swings in one period.
- In this example, the number of swings in one period is 2.
Step 2: Calculate the total number of swings in 3 periods.
- Multiply the number of swings in one period (2) by 3: 2 * 3 = 6.
- The total number of swings in 3 periods is 6.
Step 3: Determine the number of times the child swings through the equilibrium position.
- In this example, the child swings through the equilibrium position 6 times.
So, in this case, the child swings through the swing's equilibrium position a total of 6 times during the course of 3 periods of motion.
To determine how many times the child swings through the swing's equilibrium position during the course of 3 periods of motion, we need to understand what constitutes a "period" and the motion of a swing.
A period is the time it takes for one complete cycle of motion to occur. In the case of a swing, a complete cycle involves the swing moving from one extreme position (highest point) to the other extreme position and back to the starting point.
To find the number of swings through the equilibrium position, we need to know how many cycles occur in 3 periods of motion. Let's break down the steps to calculate this:
1. Determine the number of cycles in one period:
- Observe the child swinging and count the number of times the swing goes from one extreme position to the other (e.g., from highest point to lowest point and back to the highest point).
- Let's say there are n cycles in one period.
2. Calculate the number of cycles in 3 periods:
- Multiply the number of cycles in one period (n) by 3.
- The result will give you the number of swings through the equilibrium position during 3 periods of motion.
Remember, the equilibrium position of a swing is the point at which it hangs vertically without any external force acting on it.
By following these steps and determining the number of cycles in one period, you can find the total number of swings through the equilibrium position during 3 periods of motion.