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What are two classic simple harmonic oscillators?
Answer:
A simple harmonic oscillator is any system that when displaced from equilibrium wil satisfy the equation
F=-kx
Where F is the force (mass times acceleration), k is a constant, and x is the position of the oscillator.
The classical example of a harmonic oscillator is the mass on a spring. When you displace the mass, the spring will cause the mass to oscillate back and forth in the direction of the string. In this case, k is the spring constant, a value that effectively tells you how stiff the spring is.
The second classical example is the small angle pendulum. When you move the mass on the end of a pendulum by a small amount, gravity will pull it back towards the lowest point and create an infinite oscillation. The k in this example is equal to m*g/l where m is the mass of the end of the pendulum, g is the acceleration due to gravity (9.81m/s²) and l is the length of the pendulum.
In reality however, these systems rarely display simple harmonic motion. Due to the effects of air resistance, these systems are constantly being dampened and behave in a much more complex way. In addition, the pendulum case only works for small angles due to an approximation used in the derivation of the formula. Anything more than about 10 degrees and the equation will soon stop describing the actual motion.
F=-kx
Where F is the force (mass times acceleration), k is a constant, and x is the position of the oscillator.
The classical example of a harmonic oscillator is the mass on a spring. When you displace the mass, the spring will cause the mass to oscillate back and forth in the direction of the string. In this case, k is the spring constant, a value that effectively tells you how stiff the spring is.
The second classical example is the small angle pendulum. When you move the mass on the end of a pendulum by a small amount, gravity will pull it back towards the lowest point and create an infinite oscillation. The k in this example is equal to m*g/l where m is the mass of the end of the pendulum, g is the acceleration due to gravity (9.81m/s²) and l is the length of the pendulum.
In reality however, these systems rarely display simple harmonic motion. Due to the effects of air resistance, these systems are constantly being dampened and behave in a much more complex way. In addition, the pendulum case only works for small angles due to an approximation used in the derivation of the formula. Anything more than about 10 degrees and the equation will soon stop describing the actual motion.
First answer by Megabnx.
Last edit by Megabnx.
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