# Class 11 Physics Oscillations: NCERT Solutions for Question 4

This page focuses on the detailed Oscillations question answers for Class 11 Physics Oscillations, addressing the question: '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 (ω is any positive constant): (a) sin ωt - cos wt (b) sin3 ωt (c) 3 cos (π/4 - 2ωt) (d) cos ωt +  cos 3ωt + cos 5ωt (e) exp (-ω2t2)'. The solution provides a thorough breakdown of the question, highlighting key concepts and approaches to arrive at the correct answer. This easy-to-understand explanation will help students develop better problem-solving skills, reinforcing their understanding of the chapter and aiding in exam preparation.
Question 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 (ω is any positive constant):(a) sin ωt - cos wt(b) sin3 ωt(c) 3 cos (π/4 - 2ωt)(d) cos ωt +  cos 3ωt + cos 5ωt(e) exp (-ω2t2)

(a) SHM

The given function is:

sin ωt - cos wt

= underroot 2 [1/underroot 2 sin ωt - 1/underroot 2 cos ωt]

= underroot 2 [ sin ωt  x cos π/4 - cos ωtx cos π/4]

= underroot 2 ( ωt - π/4)

This function represents SHM as it can be written in the form:

a sin ( ωt  + ø )

Its period is: 2π/ω

(b) Periodic, but not SHM

The given function is:

sin3ωt = ¼ [3sin ωt –sin 3ωt]
Even though the two sin ωt represent simple harmonic motions respectively, but they are periodic because superposition of two SIMPLE HARMONIC MOTION is not simple harmonic.

(c) 3 cos (π/4 – 2ωt) = 3 cos (2ωt – π/4)
As it can be written as : a sin ( ωt  + Φ) , it represents SIMPLE HARMONIC MOTION
Its period is : π/ω

(d) In cos ωt + cos 3ωt + cos 5ωt, each cosine function represents SIMPLE HARMONIC MOTION, but the super position of SIMPLE HARMONIC MOTION gives periodic.

(e) As it is an exponential function, it is non periodic as it does not repeat itself.

( f ) 1 + ωt + ω2 t2 is non periodic.