Question

Which of the following figure represents damped harmonic motion

Answer 1

Hint:Here four graphs for the damped harmonic motion are given and asked which one is the correct one. For this we need to find the relation between the given quantity in the graph in case of damped harmonic motion. That is what happens to amplitude and displacement of the object with time.




Complete answer:
We know that a damped harmonic motion is a simple harmonic motion where the amplitude of the object in motion keeps on decreasing with the passage of time. Energy of the given system dissipates continuously because the oscillations fade away with time.
If we take an example of a swinging clock pendulum, we see how the amplitude keeps on decreasing when an external force is applied.
Now, from the above given option;
Option B is wrong as the amplitude increases with time in that graph shown, so it is not damped harmonic motion.
Same is with option C also amplitude increases with time.
Option D is also wrong as the decrease in amplitude is sudden, that is not the case of damped harmonic motion.
We can clearly see that the Option A resembles the case of swinging clock pendulum. Here the amplitude keeps on decreasing with the passage of the time. Also the displacement becomes zero at last and the body comes at rest.

Hence, the correct answer is Option A.


Note:Damped harmonic motion is a type of simple harmonic motion with damped oscillations that is amplitude of the object in motion keeps on decreasing with time but in harmonic form not the sudden change in amplitude. It will be in equal amounts as in the harmonic case.