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Identify the periodic functions and their time periods, if any from the following (i) sin 2t , (ii) sin 3t , (iii) sint + cos t , (iv) sin t + sin 3t (v) e^(-1)

Answer» <html><body><p></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :If can be written as `sin <a href="https://interviewquestions.tuteehub.com/tag/2t-301164" style="font-weight:bold;" target="_blank" title="Click to know more about 2T">2T</a> = sin (2t + 2pi) = sin 2(t+ pi)` <br/>Comparing with equation 5.1, time period of given function is `pi` units. <br/>(ii) `sin 3t = sin (3t + 2pi) sin 3 (t+ (2pi)/(3)) therefore ` Time period , `T= (2pi)/(3)` <br/>(iii) After trigonometric transformations, the given functions can be written as<br/>`sin t + <a href="https://interviewquestions.tuteehub.com/tag/cos-935872" style="font-weight:bold;" target="_blank" title="Click to know more about COS">COS</a> t = sqrt2 sin [omega t + pi/4]` , Since it is a sine function , its time period is also `2pi`<br/>Note that the linear combination of time and <a href="https://interviewquestions.tuteehub.com/tag/cosine-936114" style="font-weight:bold;" target="_blank" title="Click to know more about COSINE">COSINE</a> functions , such as `f(t) = A sint + B cost ` is also periodic of time period `2pi` <br/>(<a href="https://interviewquestions.tuteehub.com/tag/iv-501699" style="font-weight:bold;" target="_blank" title="Click to know more about IV">IV</a>) The time period of sin t and sin 3t are `2pi and 2pi//3` as already discussed in above examples . Since the given function can repeat it self only after a time of `2pi` , its time period is `2pi` . <br/>(v)The plot of `e^(-1)` vs t is an shown<br/>From the graph , it is easy to say that the given function is not periodic . <br/> <img src="https://doubtnut-static.s.llnwi.net/static/physics_images/AKS_ELT_AI_PHY_XI_V01_C_C05_SLV_002_S01.png" width="80%"/></body></html>


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