a child on a swing goes backwards and forwards 100 times in 5 minutes. calculate period of the oscillation and freuency in hertz.
20s
20 second
Well, if a child on a swing goes backwards and forwards 100 times in 5 minutes, we can calculate the period of the oscillation.
Period is defined as the time it takes for one complete cycle of oscillation. In this case, one complete cycle consists of swinging forward and swinging backward. So, the child swings back and forth 100 times, meaning they complete 100 cycles.
Since we know the time taken is 5 minutes, we can calculate the period as:
Period = Total time taken / Number of cycles
= 5 minutes / 100 cycles
Now, let's convert the time to seconds to make the calculations easier. There are 60 seconds in a minute, so:
Period = (5 minutes * 60 seconds) / 100 cycles
= 300 seconds / 100 cycles
= 3 seconds per cycle
So, the period of the oscillation is 3 seconds.
Now, to calculate the frequency in hertz, we can use the formula:
Frequency (in Hz) = 1 / Period
Frequency = 1 / 3 seconds per cycle
= 0.33 Hz
Therefore, the frequency of the child's oscillation on the swing is approximately 0.33 Hz.
To calculate the period and frequency of the oscillation, we first need to understand the definitions of these terms:
1. Period: The period is the time it takes for one complete cycle of an oscillation. It is usually measured in seconds.
2. Frequency: The frequency is the number of complete cycles or oscillations that occur per unit of time. It is usually measured in hertz (Hz), which represents the number of cycles per second.
Given that the child on a swing goes backwards and forwards 100 times in 5 minutes, we can use this information to calculate the period and frequency.
To calculate the period:
1. Convert 5 minutes to seconds: 5 minutes * 60 seconds/minute = 300 seconds.
2. Divide the total time (300 seconds) by the number of oscillations (100) to find the period: 300 seconds / 100 oscillations = 3 seconds.
So, the period of the oscillation is 3 seconds.
To calculate the frequency:
1. Divide the number of oscillations (100) by the total time in seconds (300 seconds): 100 oscillations / 300 seconds = 0.3333 oscillations/second.
Since frequency is measured in hertz (Hz), we need to round the result:
2. Round the result to two decimal places: 0.3333 ≈ 0.33 Hz.
So, the frequency of the oscillation is approximately 0.33 Hz.