Question

Which of the following energy-time graphs represents a damped harmonic oscillator?
(A)

(B)

(C)

(D)

Answer 1

Hint: To solve this question we will first understand the meaning and significance of harmonic oscillators. A harmonic oscillator is considered as a physical system in which some values or quantities oscillate to and fro or above and below from a mean value at one or more than one characteristic frequencies.

Complete Step-by-step solution
A harmonic oscillator is very important and shows significant properties because it provides an approximate solution of nearly every system with minimum potential energy which is considered as harmonic oscillator potential. A simple example of a harmonic oscillator is a simple pendulum. Small clocks and radio circuits also work on the principle of the harmonic oscillator.
Now we will discuss the damped harmonic oscillator which can be defined as a vibrating system in which the amplitudes of the vibrations decrease over time. If we observe then we can find that nearly every physical system act as a damped harmonic oscillator.
As discussed, in the case of the damped harmonic oscillator the amplitude of the oscillations reduces over time. Hence if we observe the energy-time graph of the damped harmonic oscillator it can be seen that as time passes then the energy of the system reduces.

Therefore from the given options, the only valid option that matches is an option (A).
Hence the option (A) is the correct answer.

Note
We can observe examples of the damped harmonic oscillator in our day to day life such as a YO-YO, clock pendulum, and guitar strings. In the case of all these examples, it can be seen that oscillations tend to slow down over time.