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16.3 Simple Harmonic Motion: A Special Periodic Motion
The period found in (b) is the time per cycle, but this value is often quoted as simply the time in convenient units.
You can identify an event in your life that occurs frequently.
The net force that can be described by Hooke's law is very common.
They are the simplest systems.
The units for displacement and amplitude are the same.
For the object on the spring, the units of amplitude and displacement are meters; whereas for sound oscillations, they have units of pressure.
The energy in the oscillation is related to the maximum displacement.
There is a bowl or basin that is shaped like a hemisphere.
Place a marble inside the bowl and tilt the bowl so the marble rolls from the bottom of the bowl to the high points on the sides of the bowl.
This periodic motion requires force to maintain it.
An object attached to a spring sliding on a surface is a simple harmonic oscillator.
The object performs simple motion when it is displaced from equilibrium.
As it passes through equilibrium, the object's maximum speed occurs.
The period is smaller when the spring is stiff.
The period is affected by the mass of the object.
There is a special thing about the period and frequencies of a simple harmonic oscillator.
The string of a guitar can be plucked gently or hard.
The period is constant, so a simple harmonic oscillator can be used as a clock.
There are two important factors that affect the period.
The period is related to how stiff the system is.
The system has a smaller period because of the stiff object.
You can adjust a diving board's stiffness, for example, if you want it to vibrate quicker.
Period is dependent on the mass of the system.
The longer the period, the bigger the system is.
A heavy person on a diving board bounces up and down more slowly than a light person.
The mass and force constant are the only factors that can affect the period and frequencies of simple motion.
There is no dependence on amplitude.
If you want the length of the ruler that protrudes from the table to be the same, tape one end of the ruler to the edge of the table.
Measure the period of oscillation of each of the rulers bylucking the ends of the rulers at the same time and observing which one undergoes more cycles in a time period.
The equation states that the car's oscillations will be similar to a simple harmonic oscillator.
The mass and force constant are given.
The values seem right for a bouncing car.
If you push down hard on the end of the car, you can see the oscillations.
Figure 16.11 shows an object bouncing on a spring as it leaves a wavelike "trace of its position on a moving strip of paper."
Both waves have functions.
Simple motion is related to the waves.
The bouncing car is moving.
The wave is a function if the restoring force in the suspension system can be described by Hooke's law.
The vertical position of an object bouncing on a spring is recorded on a strip of moving paper.
The correct direction for the velocity is given by the minus sign in the first equation.
The system is moving back toward the equilibrium point after the start of the motion.
We can use the second law to get an expression for acceleration.
The second law states that the acceleration is.
It is proportional to and in the opposite direction.
The net force on the object can be described by Hooke's law.
The initial position has the vertical displacement at its maximum value, which is negative as the object moves down, and the initial acceleration is negative, back toward the equilibrium position.
The most important point is that the equations are easy to understand and valid for all simple motion.
They are useful in showing how waves add with one another.
The period and Frequency have not changed.
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