Asked by debojyoti
                period of
x(t)=10 sin(12 pi t)+4 cos(18 pi t)
            
        x(t)=10 sin(12 pi t)+4 cos(18 pi t)
Answers
                    Answered by
            Steve
            
    sin 12πt has period 2π/12π = 1/6
cos 18πt has period 2π/18π = 1/9
So, the sum has period LCM(1/6,1/9) = 1/3
You can see this at
http://www.wolframalpha.com/input/?i=10+sin%2812+pi+t%29%2B4+cos%2818+pi+t%29+
    
cos 18πt has period 2π/18π = 1/9
So, the sum has period LCM(1/6,1/9) = 1/3
You can see this at
http://www.wolframalpha.com/input/?i=10+sin%2812+pi+t%29%2B4+cos%2818+pi+t%29+
                    Answered by
            Reiny
            
    period of first = 2π/(12π) = 1/6
period of 2nd = 2π/(18π) = 1/9
1/3 is a factor of both, so the
period = 1/3
verification:
http://www.wolframalpha.com/input/?i=10+sin%2812+pi+t%29%2B4+cos%2818+pi+t%29
    
period of 2nd = 2π/(18π) = 1/9
1/3 is a factor of both, so the
period = 1/3
verification:
http://www.wolframalpha.com/input/?i=10+sin%2812+pi+t%29%2B4+cos%2818+pi+t%29
                    Answered by
            Reiny
            
    Steve, that is really scary. 
    
                    Answered by
            Steve
            
    what can I say?
    
                    Answered by
            lalithsugumar
            
    for 1/6 and 1/9 the L.C.M isn`t 1/3
    
                                                    There are no AI answers yet. The ability to request AI answers is coming soon!
                                            
                Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.