A 300 g oscillator has a speed of 95.4 cm/s when its displacement is 3.00 cm and 71.4 cm/s when its displacement is 6.00 cm. What is the oscillator's maximum speed? Thank you!
Tiit
10
To find the oscillator's maximum speed, we need to understand the relationship between displacement and speed for an oscillator.
An oscillator goes through periodic motion, usually in the form of oscillations, which can be visualized on a graph known as a displacement-time graph. In this graph, displacement is plotted on the y-axis, and time is plotted on the x-axis.
The speed of the oscillator at any given point is determined by the slope of the displacement-time graph at that point. The steeper the slope, the higher the speed, and the flatter the slope, the lower the speed.
In this problem, we are given two points on the displacement-time graph: (3.00 cm, 95.4 cm/s) and (6.00 cm, 71.4 cm/s).
To find the maximum speed, we need to determine the point on the graph with the steepest slope, which corresponds to the point where the oscillator is at its maximum displacement.
We can calculate the slope between the two given points using the equation:
slope = (change in displacement) / (change in time)
In this case, the change in displacement is 6.00 cm - 3.00 cm = 3.00 cm, and the change in time is unknown. However, we don't need the actual values of time, as we are only interested in the relative change in slope. So, we can ignore the time values and focus solely on the displacement values.
The slope between the two points is:
slope = (change in displacement) / (change in time) = (3.00 cm) / (change in time)
Now, let's compare this slope with the slope between the maximum displacement point and one of the given points (3.00 cm, 95.4 cm/s).
Since the maximum displacement point has a displacement of 6.00 cm, the slope between this point and (3.00 cm, 95.4 cm/s) is:
slope = (change in displacement) / (change in time) = (6.00 cm - 3.00 cm) / (change in time) = 3.00 cm / (change in time)
Comparing the two slopes, we can see that they are equal:
(3.00 cm) / (change in time) = 3.00 cm / (change in time)
This means that the maximum speed occurs at the point where the oscillator's displacement is 6.00 cm. In other words, the speed of 71.4 cm/s is the maximum speed of the oscillator.
Therefore, the oscillator's maximum speed is 71.4 cm/s.