Chapter 10

SIMPLE HARMONIC MOTION

PREVIEW

An object such as a pendulum or a mass on a spring is oscillating or vibrating if it is moving in a repeated path at regular time intervals. We call this type of motion harmonic motion. For an object to continue oscillating there must be a restoring force continually trying to restore it to its equilibrium position. For, the force exerted by an ideal spring obeys Hooke’s law. As an object in simple harmonic motion oscillates, its energy is repeatedly converted from potential energy to kinetic energy, and vice – versa.

The content contained in sections 1, 2, 3, and 4 of chapter 10 of the textbook is included on the AP Physics B exam.

QUICK REFERENCE

Important Terms

amplitude*…show more content…*

For an ideal spring, the stretch is proportional to the force, but in the opposite direction. If we pull with twice the force, the spring will stretch twice as far.

The graph below represents the magnitude of the force F vs stretched length x for a spring:

The slope of the line is the change in force (rise) divided by the change in length (run). Since this ratio is also equal to the spring constant k, the higher slope of the graph the higher the spring constant, which is an indication of the stiffness of the spring.

We can find the spring constant k for this spring by taking the ratio of the force to the stretch for a particular interval. In other words, we can find the slope of the F vs. x graph for each spring. The slope of the line and the spring constant for spring is 50 N/m.

As on any other F vs. x graph, the work done in stretching or compressing the spring to a certain displacement can be found by finding the area under the graph. The total work done in stretching this spring is

10.2 Simple Harmonic Motion and the Reference Circle

In the equation for the spring force above, x is the displacement from equilibrium position at any time. Because of the oscillatory nature of the vibrating mass, we can express the displacement x from equilibrium position at any time t as or where A is the amplitude of oscillation and (the lower case Greek

SIMPLE HARMONIC MOTION

PREVIEW

An object such as a pendulum or a mass on a spring is oscillating or vibrating if it is moving in a repeated path at regular time intervals. We call this type of motion harmonic motion. For an object to continue oscillating there must be a restoring force continually trying to restore it to its equilibrium position. For, the force exerted by an ideal spring obeys Hooke’s law. As an object in simple harmonic motion oscillates, its energy is repeatedly converted from potential energy to kinetic energy, and vice – versa.

The content contained in sections 1, 2, 3, and 4 of chapter 10 of the textbook is included on the AP Physics B exam.

QUICK REFERENCE

Important Terms

amplitude

For an ideal spring, the stretch is proportional to the force, but in the opposite direction. If we pull with twice the force, the spring will stretch twice as far.

The graph below represents the magnitude of the force F vs stretched length x for a spring:

The slope of the line is the change in force (rise) divided by the change in length (run). Since this ratio is also equal to the spring constant k, the higher slope of the graph the higher the spring constant, which is an indication of the stiffness of the spring.

We can find the spring constant k for this spring by taking the ratio of the force to the stretch for a particular interval. In other words, we can find the slope of the F vs. x graph for each spring. The slope of the line and the spring constant for spring is 50 N/m.

As on any other F vs. x graph, the work done in stretching or compressing the spring to a certain displacement can be found by finding the area under the graph. The total work done in stretching this spring is

10.2 Simple Harmonic Motion and the Reference Circle

In the equation for the spring force above, x is the displacement from equilibrium position at any time. Because of the oscillatory nature of the vibrating mass, we can express the displacement x from equilibrium position at any time t as or where A is the amplitude of oscillation and (the lower case Greek

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