Question

An object having mass m is attached to a spring of force constant k oscillates with simple harmonic motion. The total mechanical energy of the system is E and the maximum displacement from equilibrium is A. What is the system's potential energy when its kinetic energy is equal to 3/4E?
What is the system's potential energy when its kinetic energy is equal to ?
1. kA2
2. kA2/2
3. kA2/4
4. kA2/8

Answer 1

Answer:

The potential energy of the system is $\dfrac{E}{4}$.

Explanation:

Given :

Mass of object , m .

Spring constant , k .

Total energy , E .

Maximum displacement , A .

We have to find potential energy when its kinetic energy is equal to 3/4E .

Now, we know :

Total energy is constant in simple harmonic motion.

Therefore ,

Total energy = Kinetic energy + potential energy .

$E=P.E+\dfrac{3E}{4}\\\\P.E=\dfrac{E}{4}$

Hence , this is the required solution.