The image shows a graph of a periodic function $x(t)$ representing oscillations. The task is to determine the frequency (in Hz) based on the graph.

Steps to Determine the Frequency:

1. Identify the Period $T$: The period $T$ is the time it takes for one complete cycle of the oscillation. From the graph, locate two consecutive points where the wave pattern repeats (e.g., from peak to peak or trough to trough).

2. Calculate the Frequency $f$: The frequency $f$ is the inverse of the period $T$, given by the formula: $f = \frac{1}{T}$

Let's analyze the graph:

• The time between two consecutive peaks (or troughs) corresponds to the period $T$.
• On the x-axis, the time is labeled as $t_1, t_2, t_3, t_4$, etc.

From the image, if we consider the points where the function crosses the x-axis and repeat, for instance:

• $t_2$ to $t_4$ represents one full cycle.
• If the difference between $t_2$ and $t_4$ is $T$, then the frequency $f$ is $\frac{1}{T}$.

Now, we just need the numerical value of $T$ from the graph to compute the frequency. However, based on the graph layout, if we assume the units on the x-axis are in seconds, and the period $T$ (time difference between two peaks or troughs) is known, the frequency would be:

$f = \frac{1}{T}$

For an accurate frequency value, please provide the time intervals on the x-axis or the period $T$.

Do you have any further questions or need details on any specific part?

Related Questions:

1. What is the relationship between angular frequency and period?
2. How does the amplitude of the oscillation affect the graph?
3. What other methods can be used to determine the frequency of a signal?
4. Can the frequency be determined if the graph has noise? How?
5. How would the graph change if the frequency doubled?

Tip:

Always check the axis labels and units when analyzing graphs to ensure accuracy in calculations and interpretations.