10.1.1 A Mass on a Spring: Simple Harmonic Motion

Question 1

A Mass on a Spring: Simple Harmonic Motion

Answer 1

• An object that oscillates about a point of equilibrium executes what is called harmonic motion. This type of motion is very common in nature. The most fundamental form of harmonic motion is called simple harmonic motion.
• The position of an object in simple harmonic motion is described by a cosine curve: .
• Four quantities useful in describing simple harmonic motion are the amplitude (A), period (T), frequency (¦), and angularfrequency (v).

Question 2

Consider the graph. Which of the following lists the amplitude, the period, and the angular frequency in order?

Answer 2

5.00 cm, 5.00 s, 0.4 pi rad/s

Question 3

Which of the following is an example of simple harmonic motion (SHM)?

Answer 3

A suspension bridge oscillating after an initial burst of wind.

Question 4

After a gust of wind, a building begins oscillating with a period of 2.05 s. Moving from one maximum to the other displaces the top of the building 3.00 m. If timing begins when the wind first strikes the building (the building is at equilibrium), which of the following equations represents the building’s motion?

Answer 4

x = 1.50 m * cos (2pi*t/2.05s + pi/2)

Question 5

A small honeybee gets caught in a spider web, which then executes SHM with a period of 8.00 Hz. Assuming a maximum positive displacement at t=0 of x = 5.25 mm, what is the bee’s position at t = 3.00s?

Answer 5

−3.71 mm

Question 6

A piece of oak is dropped onto a smooth pond and settles into SHM (ignoring friction) after a few seconds. A bored fisherman’s son times the bobbing oak with his amazing new oak bob timing apparatus, measuring 0.200 s for the oak to travel a total distance of 3.00 cm from its lowest position to its highest position. If this timing is started at the bottom of the oscillation, which the boy counts as negative x, which of the following is the block’s position after 2.50 s?

Answer 6

0.00 cm

Question 7

A student filmed herself bungee jumping for a physics project. Using her sharply honed physics skills, she is able to make the following measurements of her own SHM. When the timing starts, the total length of travel from bottom to top of the oscillation is 10.0 m, and the total time for this travel is 5.25 s. Which of the following is the student’s equation of motion?

Answer 7

x = 5.00 m * cos(2pi/10.5s)

Question 8

In dynamics, you learned the equation x(t) = x0 + v0t + 1/2at^2 for one dimension. Now, for simple harmonic motion, you learned x(t) = A cos(wt + theta). Which of the following relates the reason for this change?

Answer 8

The force, and therefore the acceleration, is not constant.

Question 9

The motion of a long-distance runner traveling around a circular quarter-mile track is very similar to SHM. If the runner completes one mile in 5 minutes, which of the following is his frequency?

Answer 9

1.33*10^-2 s^-1

Question 10

A tuning fork, designed for 512 Hz, oscillates with SHM having a maximum displacement of 1.50 mm from the equilibrium. If timing begins at maximum displacement, which of the following is the equation governing the motion of the tuning fork?

Answer 10

x = 1.50 mm * cos (1024pi rad/s * t)