Question

Which of the following quantity does not change due to damping of oscillations?

A. Angular frequency
B. Time period
C. Initial phase
D. Amplitude

Answer 1

Hint:First of all start with knowing what is damping oscillations and then use method of elimination and check each options one by one in case of damping oscillation and find whether which of the above option will get changed or remains unchanged due to damping oscillation.




Formula used
1. $\omega = 2\pi f$
Where, $\omega $ is the angular frequency
And f is linear frequency
2. $f = \dfrac{1}{T}$
Where, T is time period




Complete answer:

First we need to know what is damping of oscillations:
A damped oscillation is where a frictional force or resistance force is applied which causes change in motion of the body that means an oscillation that fades away with time.
Take an example of a swinging pendulum and find out which of the above quantities change due to damping of oscillations.
For option A: we know that;
Angular frequency, $\omega = 2\pi f$
Also, frequency $f = \dfrac{1}{T}$
It means frequency depends on time.
Time will increase when resistance force is applied on the pendulum.
So, angular frequency also depends on time. Therefore, angular frequency will change in case of damping oscillations.
For option B: time period will increase.
For option C: Initial phase let $\theta $ from which the pendulum was released does not depends on medium or resistance force. Therefore, it will not change.
For option D: Amplitude will keep on decreasing as the $\theta $ will decrease with time.

Hence, the correct answer is Option C.



Note:You need to know about all the quantities given in the options and then find all conditions on which it depends on and then only use the method of elimination. Also here we have taken the help of an example of damping oscillation in case of swinging pendulum.