Question

Which of the following properties should remain fixed for an undamped oscillation of the body?
A. Acceleration
B. Phase
C. Amplitude
D. Velocity

Answer 1

Hint: The acceleration is found to be proportional to the displacement from the mean position. When the body is displaced to the extreme position, the velocity at that time will be zero. When the body is reached to the mean position the velocity will be maximum at the centre. For the oscillations to be undamped, it will go to the similar extreme location each time. This will help you in answering this question.

Complete step-by-step answer:
As we all know that the acceleration is found to be proportional to the displacement from the mean position. This clearly mentions that this quantity will be changing accordingly. Therefore the option A will not be the correct answer. Now let us look at velocity. The velocity is also found to be changing when it is displaced from its mean position. When the body is displaced to the extreme position, the velocity at that time will be zero. When the body is reached to the mean position the velocity will be maximum at the centre. Therefore this will be not the correct answer. Now let us look at the phase of the oscillation. It has been found that the phase is also varying. But for the oscillations to be undamped, it will go to the similar extreme location each time. Therefore as the phase will also be changing this will not be the correct answer. Only the amplitude should be a constant in an undamped oscillation. Therefore the correct answer will be the amplitude. This has been mentioned as option C.

So, the correct answer is “Option C”.

Note: The acceleration is defined as the rate of variation of velocity with respect to time taken. The velocity has been found by taking the rate of variation of displacement of the body with respect to time taken. Both these quantities are found to be vectors. A vector is a quantity which is having both magnitude as well as direction.