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NCERT Class 11 Physics Solutions: Chapter 14 β Oscillations-Part 2
Question 14.3:
Figure depicts four plots for linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion) ?
Answer:
Are periodic
Explanation:
It is not a periodic motion. This represents a unidirectional, linear uniform motion. There is no repetition of motion in this case.
In this case, the motion of the particle repeats itself after Hence, it is a periodic motion, having a period of
It is not a periodic motion. This is because the particle repeats the motion in one position only. For a periodic motion, the entire motion of the particle must be repeated in equal intervals of time.
In this case, the motion of the particle repeats itself after . Hence, it is a periodic motion, having a period of
Question 14.4:
Which of the following functions of time represent,
(a) Simple harmonic,
(b) Periodic but not simple harmonic, and
(c) Non-periodic motion?
Give period for each case of periodic motion ( is any positive constant) :
Answer:
: Simple harmonic motion
Explanation:
The given function is:
This function represents SHM as it can be written in the form:
Its period is:
:
Periodic, but not Simple harmonic motion
Explanation:
The given function is:
The terms individually represent simple harmonic motion.
However, the superposition of two simple harmonic motion is periodic and not simple harmonic.
:
Simple harmonic motion.
Explanation:
The given function is:
This function represents simple harmonic motion because it can be written in the form:
Its period is:
: Periodic, but not simple harmonic motion
Explanation:
The given function is . Each individual cosine function represents simple harmonic motion. However, the superposition of three simple harmonic motions is periodic, but not simple harmonic.
: Non-periodic motion
Explanation:
The given function is an exponential function. Exponential functions do not repeat themselves. Therefore, it is a non-periodic motion.
:
The given function is non-periodic.