The angle of pendulum from straight down will vary in a sinusoidal fashion as it swings. In Physics you will learn (if you haven't already) that for a frictionless pendulum, released k radians from feet vertical will be 0 (t) = k cos (t). g is gravitational acceleration, on Earth's surface~32 s2 %3D For our problem the length is 20 inches, which will require conversion to be the L in the equation. We will use k = 0.15 radians.

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Chapter1: Units, Trigonometry. And Vectors
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2d and 2f answered please

3) The angle of pendulum from straight down will vary in a sinusoidal fashion as it swings. In Physics
you will learn (if you haven't already) that for a frictionless pendulum, released k radians from
feet
vertical will be 0 (t)
= k cos
(t). gis gravitational acceleration, on Earth's surface ~32
s2.
For our problem the length is 20 inches, which will require conversion to be the L in the equation.
We will use k = 0.15 radians.
а.
Find the angular frequency (w) of the oscillation.
L = 20 in.
e = 0.15 rad
b. Find the period in seconds.
Find the time until (t) = 0. (ie when it is straight down)
С.
d. Plot one complete cycle of the waveform by hand. Be sure to label the amplitude and period
on the plot.
e. Using a software tool, confirm your calculations and plot the function over one cycle.
Confirm that it agrees with your hand plot.
f.
Suppose we had chosen to write the pendulum equation using a sine function instead of a
cosine. What phase offset would we have to add to get the same behavior?
Transcribed Image Text:3) The angle of pendulum from straight down will vary in a sinusoidal fashion as it swings. In Physics you will learn (if you haven't already) that for a frictionless pendulum, released k radians from feet vertical will be 0 (t) = k cos (t). gis gravitational acceleration, on Earth's surface ~32 s2. For our problem the length is 20 inches, which will require conversion to be the L in the equation. We will use k = 0.15 radians. а. Find the angular frequency (w) of the oscillation. L = 20 in. e = 0.15 rad b. Find the period in seconds. Find the time until (t) = 0. (ie when it is straight down) С. d. Plot one complete cycle of the waveform by hand. Be sure to label the amplitude and period on the plot. e. Using a software tool, confirm your calculations and plot the function over one cycle. Confirm that it agrees with your hand plot. f. Suppose we had chosen to write the pendulum equation using a sine function instead of a cosine. What phase offset would we have to add to get the same behavior?
Expert Solution
Step 1

As per your request, we will solve the part d and f only.

 

Given that:

L=20 inch=1.67 ft      [ 1ft=12 inch]k= 0.15 radθ=k cos (gLt)

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