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

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?

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  

it doesn't. it was imagined up in the middle ages.