# Find Amplitude of Glider in Air-Track Oscillation

• Liketothink
In summary, the conversation discusses the oscillation of an air-track glider attached to a spring, completing 27 oscillations in 44.7 seconds between the marks of 9.23 cm and 50.23 cm. The question asks for the angular frequency of the glider, which is found to be 3.7933 rad/s. The amplitude of the glider is also discussed, with the conclusion that it is equal to half the distance the glider travels, which is 20.5 cm. The conversation also mentions a related problem about amplitude, but no solution is provided.
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## Homework Statement

An air-track glider attached to a spring oscillates between the 9.23 cm mark and the 50.23 cm mark on the track. The glider completes 27 oscillations in 44.7 s. angular frequency of the glider? (in rad/s)
3.7933
what is the amplitude of the glider?

x=Acos(wt+ro)

## The Attempt at a Solution

I considered that at x=9.23 the amplitude was zero and so is ro.
Hence, x=50.23 would equal just 50.23 cm=Acos(3.79(44.7)). But A turned out to be negative. What am I doing wrong? How do I solve this problem? Thank you in advance.

What is the center of oscillation here? The amplitude is the maximum distance from the center that the glider reaches.

Would it be half the distance the glider travels which is 20.5 cm?

Correct.

It still gives me a negative number if I do .205/((cos(3.79*44.7)).

Negative number for what?

For the amplitude A.

You just said the amplitude was 20.5 cm, which is correct.

OH! Ok I get it. Thank you very much.

## 1. How is the amplitude of a glider in air-track oscillation measured?

The amplitude of a glider in air-track oscillation is measured by finding the maximum displacement of the glider from its equilibrium position. This can be done by using a ruler or a motion sensor to track the movement of the glider over a period of time.

## 2. What factors affect the amplitude of a glider in air-track oscillation?

The amplitude of a glider in air-track oscillation is affected by the initial displacement of the glider, the mass of the glider, and the spring constant of the air-track. Other factors such as air resistance and friction may also have an impact on the amplitude.

## 3. How does the amplitude of a glider in air-track oscillation change over time?

The amplitude of a glider in air-track oscillation will decrease over time due to energy being lost to factors such as air resistance and friction. This is known as damping. The rate at which the amplitude decreases depends on the initial conditions and the properties of the air-track.

## 4. Can the amplitude of a glider in air-track oscillation be changed?

Yes, the amplitude of a glider in air-track oscillation can be changed by altering the initial conditions, such as the initial displacement or the mass of the glider. The amplitude can also be changed by adjusting the properties of the air-track, such as the spring constant.

## 5. What is the relationship between amplitude and frequency in air-track oscillation?

The amplitude and frequency in air-track oscillation are inversely proportional. This means that as the frequency increases, the amplitude decreases, and vice versa. This relationship is known as the amplitude-frequency relationship and is governed by the properties of the air-track and the initial conditions of the glider.

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