lab2-extra¶
Additional tasks that exercise our current skill set. swing_time()
relates to the harmonic oscillator and exercises implementing functions.
geometric_mean2() introduces a different way of computing the mean of
two numbers. geometric_mean() generalises this to an arbitrary number
of numbers.
swing_time(L)¶
Write a function swing_time(L) that computes and returns the time
T [in seconds] needed for an idealized pendulum of length L [in
meters] to complete a single oscillation, using the equation
Example:
In [ ]: swing_time(1)
Out[ ]: 2.0060666807106475
geometric_mean2(a, b)¶
Implement a function geometric_mean2(a, b) that returns the
geometric mean of 2 numbers - i.e. the edge length a square would
have to have so that its area equals that of a rectangle with sides a
and b. You can use \(\sqrt{a b}\) to compute the geometric mean of
\(a\) and \(b\).
Examples:
>>> geometric_mean2(2, 2)
2.0
>>> geometric_mean2(2, 8)
4.0
>>> geometric_mean2(2, 1)
1.4142135623730951
Examples (IPython):
In [ ]: geometric_mean2(2, 2)
Out[ ]: 2.0
In [ ]: geometric_mean2(2, 8)
Out[ ]: 4.0
In [ ]: geometric_mean2(2, 1)
Out[ ]: 1.4142135623730951
geometric_mean(xs)¶
Implement a function geometric_mean(xs) that computes the geometric
mean of the numbers given in the list xs. The geometric mean of
\(n\) numbers \(x_1, x_2, \ldots, x_n\) is given by
\(\left(\prod_{i=1}^n x_i\right)^{\frac{1}{n}} = \sqrt[n]{x_1 \cdot x_2 \cdot \ldots \cdot x_n}\).
Example:
In [ ]: geometric_mean([1, 2])
Out[ ]: 1.4142135623730951
In [ ]: geometric_mean([1, 2, 3])
Out[ ]: 1.8171205928321397
In [ ]: geometric_mean([1, 1, 1])
Out[ ]: 1.0
Hint: Remember that a**b computes \(a^b\) (i.e. takes
a-to-the-bth-power). To compute the n-th root of a number x, you can
write x**(1/n) in Python:
In [ ]: 16**(1/2) # square root
Out[ ]: 4.0
In [ ]: 16**(1/4) # quartic root
Out[ ]: 2.0
In [ ]: 2**4
Out[ ]: 16
Please include the extra tasks in your file lab2.py
and submit as lab2 assignment.
Back to lab2.
End of lab2-extra.