The problem involves analyzing the graph of a damped oscillation and finding the amplitude after two periods from the start of the oscillation.

1. Understanding the graph: This is a graph of $x$ in cm versus $t$ in seconds, showing a damped oscillation. The amplitude decreases over time, which is typical for damped oscillations.

2. Amplitude and Period Determination:

   • The amplitude of an oscillation is the maximum displacement from the equilibrium position.
   • From the graph, the initial amplitude appears to be around 10 cm.
   • Observing the graph, we see that the period (the time it takes to complete one full oscillation) is about 3 seconds.

3. Finding the Amplitude After Two Periods:

   • Since the period is approximately 3 seconds, two periods would correspond to $2 \times 3 = 6$ seconds.
   • From the graph, we can estimate the amplitude at $t = 6$ seconds. It appears that the maximum displacement (amplitude) has decreased by this point, indicating the effect of damping.
   • Estimating from the graph, the amplitude around 6 seconds is roughly 4 cm.

Answer:

The amplitude after two periods (6 seconds) is approximately 4 cm.

Would you like further details or have any questions?

Here are 5 related questions to expand understanding:

1. What is the mathematical model for damped oscillations?
2. How does damping affect the frequency of an oscillation?
3. What are the types of damping in oscillatory motion?
4. How can you calculate the damping coefficient from an experimental graph?
5. Why does amplitude decrease in damped oscillations?

Tip: In damped oscillations, the amplitude reduction rate can often be modeled by an exponential decay function, depending on the damping coefficient.