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When we talk about the period of oscillatory motion, we are referring to the time it takes for one full cycle of motion to occur. In this context, a cycle is one full swing back and forth. Calculating the period is crucial in understanding how an oscillating object behaves over time.

To find the period (T), you need two key pieces of information: the total time taken for the oscillations and the number of oscillation cycles completed. The period can be calculated using the formula: \[ T = \frac{\text{total time}}{\text{number of cycles}} \]For the skyscraper in the given problem, it sways back and forth 95 times in 600 seconds. By dividing 600 seconds by 95 cycles, we find that each cycle takes about 6.32 seconds. This means that the period of the skyscraper's oscillation is 6.32 seconds.

Understanding the period helps in predicting when the swaying will repeat itself, which can be especially important in engineering and architecture to ensure the building's design can safely handle these movements.

Frequency is an essential concept in oscillatory motion, as it tells us how often cycles occur in a given timeframe. Frequency is measured in hertz (Hz), which is equal to one cycle per second.

To find the frequency (f) from the period (T), we take the reciprocal of the period: \[ f = \frac{1}{T} \]In our example, with a period of 6.32 seconds, the frequency of the skyscraper's oscillation is approximately 0.16 Hz. This indicates that about 0.16 cycles are completed each second.

Knowing the frequency is helpful because it provides insight into the dynamics of motion. This can be particularly useful in various applications, such as tuning musical instruments or designing systems that need to respond to specific frequencies.

Solving physics problems involves a systematic approach that helps break down complex scenarios into manageable steps. For oscillatory motion problems like the one involving the swaying skyscraper, following a clear methodology is key.

Here’s a simple problem-solving strategy:

• Understand the problem: Read the problem carefully to identify what is being asked and what information is given.
• List the known values: In the skyscraper example, these include the time frame (10 minutes) and the number of oscillations (95 cycles).
• Convert units if necessary: Always work within standard units for consistency, such as seconds for time in physics.
• Apply relevant formulas: Use formulas like \( T = \frac{\text{total time}}{\text{number of cycles}} \) for period and \( f = \frac{1}{T} \) for frequency.
• Check your calculations: Verify each step and ensure the answer makes logical sense in the context of the problem.

Following these steps not only aids in finding the correct answer but also enhances your understanding of the underlying concepts. This systematic approach can be applied across various types of physics problems, making it a versatile tool in your problem-solving toolbox.