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An object suspended from a spring vibrates with simple harmonic motion. Part A At an instant when the displacement of the object is equal to
Question
An object suspended from a spring vibrates with simple harmonic motion. Part A At an instant when the displacement of the object is equal to one-fourth the amplitude, what fraction of the total energy of the system is kinetic
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Physics
3 years
2021-08-26T19:23:02+00:00
2021-08-26T19:23:02+00:00 1 Answers
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Complete Question
An object suspended from a spring vibrates with simple harmonic motion.
a. At an instant when the displacement of the object is equal to one-half the amplitude, what fraction of the total energy of the system is kinetic?
b. At an instant when the displacement of the object is equal to one-half the amplitude, what fraction of the total energy of the system is potential?
Answer:
a
The fraction of the total energy of the system is kinetic energy
b
The fraction of the total energy of the system is potential energy
Explanation:
From the question we are told that
The displacement of the system is
where a is the amplitude
Let denote the potential energy as PE which is mathematically represented as
=>
Let denote the total energy as T which is mathematically represented as
Let denote the kinetic energy as KE which is mathematically represented as
=>
=>
Now the fraction of the total energy that is kinetic energy is
Now the fraction of the total energy that is potential energy is