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Use the Check Your Understanding questions to assess whether students achieve the learning objectives for this section. If students are struggling with a specific objective, the Check Your Understanding will help identify which objective is causing the problem and direct students to the relevant content. As an Amazon Associate we earn from qualifying purchases.
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Physics 5. My highlights. Table of contents. Chapter Review. Test Prep. Teacher Support The learning objectives in this section will help your students master the following standards: 7 Science concepts. The student knows the characteristics and behavior of waves. The student is expected to: A examine and describe oscillatory motion and wave propagation in various types of media.
In addition, the High School Physics Laboratory Manual addresses content in this section in the lab titled: Motion in Two Dimensions, as well as the following standards: 7 Science concepts. Teacher Support [BL] Review the concept of force. It stops the ruler and moves it back toward equilibrium again. From there, the motion will repeat itself. When displaced from equilibrium, the object performs simple harmonic motion that has an amplitude X and a period T.
The stiffer the spring is, the smaller the period T. The greater the mass of the object is, the greater the period T. Introduction to Harmonic Motion This video shows how to graph the displacement of a spring in the x-direction over time, based on the period. Click to view content. If the amplitude of the displacement of a spring were larger, how would this affect the graph of displacement over time? What would happen to the graph if the period was longer?
The linear displacement from equilibrium is s, the length of the arc. Teacher Support [BL] Review simple harmonic motion. Measuring Acceleration due to Gravity: The Period of a Pendulum What is the acceleration due to gravity in a region where a simple pendulum having a length What is the force constant of the spring?
What is the force constant for the suspension system of a car that settles 3. Finding Gravity Using a Simple Pendulum Use a simple pendulum to find the acceleration due to gravity g in your home or classroom. Attach a small object of high density to the end of the string for example, a metal nut or a car key. Calculate g. Accuracy for value of g will increase with an increase in the mass of a dense object.
Accuracy for the value of g will increase with increase in the length of the pendulum. The value of g will be more accurate if it maintains simple harmonic motion. What is deformation? Force Velocity Displacement Force constant. What are oscillations? Motion resulting in small displacements Motion which repeats itself periodically Periodic, repetitive motion between two points motion that is the opposite to the direction of the restoring force.
True or False—Oscillations can occur without force. True False. Teacher Support Use the Check Your Understanding questions to assess whether students achieve the learning objectives for this section. Previous Next. Search for:. Explain the link between simple harmonic motion and waves. Note that neither T nor f has any dependence on amplitude. Example 1. Calculate the Frequency and Period of Oscillations: Bad Shock Absorbers in a Car If the shock absorbers in a car go bad, then the car will oscillate at the least provocation, such as when going over bumps in the road and after stopping See Figure 2.
Check Your Understanding Part 1 Suppose you pluck a banjo string. Solution Frequency and period remain essentially unchanged. Only amplitude decreases as volume decreases. Part 2 A babysitter is pushing a child on a swing. Solution x is the maximum deformation, which corresponds to the amplitude of the wave. Click to run the simulation. Conceptual Questions What conditions must be met to produce simple harmonic motion?
Give an example of a simple harmonic oscillator, specifically noting how its frequency is independent of amplitude. Explain why you expect an object made of a stiff material to vibrate at a higher frequency than a similar object made of a spongy material. As you pass a freight truck with a trailer on a highway, you notice that its trailer is bouncing up and down slowly.
Is it more likely that the trailer is heavily loaded or nearly empty? Explain your answer. Some people modify cars to be much closer to the ground than when manufactured.
Should they install stiffer springs? What force constant is needed to produce a period of 0. If the spring constant of a simple harmonic oscillator is doubled, by what factor will the mass of the system need to change in order for the frequency of the motion to remain the same? How much mass must be added to the object to change the period to 2. By how much leeway both percentage and mass would you have in the selection of the mass of the object in the previous problem if you did not wish the new period to be greater than 2.
Suppose you attach the object with mass m to a vertical spring originally at rest, and let it bounce up and down. A diver on a diving board is undergoing simple harmonic motion. Her mass is The next diver is a male whose period of simple harmonic oscillation is 1.
What is his mass if the mass of the board is negligible? Suppose a diving board with no one on it bounces up and down in a simple harmonic motion with a frequency of 4. The board has an effective mass of What is the frequency of the simple harmonic motion of a The device pictured in Figure 6 entertains infants while keeping them from wandering.
The child bounces in a harness suspended from a door frame by a spring constant. Licenses and Attributions. CC licensed content, Shared previously. Vibrational motion is often contrasted with translational motion. In translational motion, an object is permanently displaced. The initial force that is imparted to the object displaces it from its resting position and sets it into motion. Yet because there is no restoring force, the object continues the motion in its original direction. When an object vibrates, it doesn't move permanently out of position.
The restoring force acts to slow it down, change its direction and force it back to its original equilibrium position. An object in translational motion is permanently displaced from its original position. But an object in vibrational motion wiggles about a fixed position - its original equilibrium position.
Because of the restoring force, vibrating objects do the back and forth. We will explore the restoring force in more detail later in this lesson. As you know, bobblehead dolls are not the only objects that vibrate. It might be safe to say that all objects in one way or another can be forced to vibrate to some extent. The vibrations might not be large enough to be visible. Or the amount of damping might be so strong that the object scarcely completes a full cycle of vibration.
But as long as a force persists to restore the object to its original position, a displacement from its resting position will result in a vibration. Even a large massive skyscraper is known to vibrate as winds push upon its structure.
While held fixed in place at its foundation we hope , the winds force the length of the structure out of position and the skyscraper is forced into vibration. A pendulum is a classic example of an object that is considered to vibrate. A simple pendulum consists of a relatively massive object hung by a string from a fixed support.
It typically hangs vertically in its equilibrium position. When the mass is displaced from equilibrium, it begins its back and forth vibration about its fixed equilibrium position. The motion is regular and repeating. In the next part of this lesson , we will describe such a regular and repeating motion as a periodic motion. Because of the regular nature of a pendulum's motion, many clocks, such as grandfather clocks, use a pendulum as part of its timing mechanism.
An inverted pendulum is another classic example of an object that undergoes vibrational motion. An inverted pendulum is simply a pendulum which has its fixed end located below the vibrating mass. An inverted pendulum can be made by attaching a mass such as a tennis ball to the top end of a dowel rod and then securing the bottom end of the dowel rod to a horizontal support.
This is shown in the diagram below. A gentle force exerted upon the tennis ball will cause it to vibrate about a fixed, equilibrium position. The vibrating skyscraper can be thought of as a type of inverted pendulum. Tall trees are often displaced from their usual vertical orientation by strong winds. As the winds cease, the trees will vibrate back and forth about their fixed positions.
Such trees can be thought of as acting as inverted pendula. Even the tines of a tuning fork can be considered a type of inverted pendulum. Another classic example of an object that undergoes vibrational motion is a mass on a spring.
The animation at the right depicts a mass suspended from a spring. The mass hangs at a resting position. If the mass is pulled down, the spring is stretched. Once the mass is released, it begins to vibrate. It does the back and forth , vibrating about a fixed position. If the spring is rotated horizontally and the mass is placed upon a supporting surface, the same back and forth motion can be observed.
Pulling the mass to the right of its resting position stretches the spring. When released, the mass is pulled back to the left, heading towards its resting position. After passing by its resting position, the spring begins to compress.
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