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  

answer: a. same unit

explanation: