Calculating Decay Constant of Damped Oscillations

[h6872]

Homework Statement

Marie observes damped oscillations of a glider on an air track. She observed that the amplitude decreased to 50% of its original value after 10 seconds. What is the decay constant for the motion of the glider?

Homework Equations

The Attempt at a Solution

It seems the equation including the decay constant (involving the displacement, amplitude, angular frequency, and time) seems a little overcomplicated, considering the information given for this particular example.

However, I do know that if the motion of the damped glider is plotted, then the decay constant τ can be derived from the equation τ = -log e/slope. From the information given, I know that the graph will be of an exponential function, but how do I know what the slope of it would be given a 50% reduction in 10 seconds? Please help!

 

[LowlyPion]

Homework Statement

Marie observes damped oscillations of a glider on an air track. She observed that the amplitude decreased to 50% of its original value after 10 seconds. What is the decay constant for the motion of the glider?

Homework Equations

The Attempt at a Solution

It seems the equation including the decay constant (involving the displacement, amplitude, angular frequency, and time) seems a little overcomplicated, considering the information given for this particular example.

However, I do know that if the motion of the damped glider is plotted, then the decay constant τ can be derived from the equation τ = -log e/slope. From the information given, I know that the graph will be of an exponential function, but how do I know what the slope of it would be given a 50% reduction in 10 seconds? Please help!

Won't the equation be proportional then to e^(-kt) ?

Doesn't that mean then that e^(-k*10) = 1/2 ?

What happens if you then take the natural log of both sides?