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Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, (ω is any positive constant): 3 cos πωt(π4–2ωt) - Physics

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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):

3 cos `(π/4 – 2ω"t")`

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Solution

SHM

The given function is:

`3cos[pi/4 - 2omegat]`

`= 3cos[2omegat - pi/4]`

This function represents simple harmonic motion because it can be written in the form: `acos(omegat + phi)`

Its period is `(2pi)/(2omega) = pi/omega`

Concept: Simple Harmonic Motion and Uniform Circular Motion
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APPEARS IN

NCERT Class 11 Physics
Chapter 14 Oscillations
Exercises | Q 4.3 | Page 358
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