Question
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
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+
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
Reiny
Steve, that is really scary.
Steve
what can I say?
lalithsugumar
for 1/6 and 1/9 the L.C.M isn`t 1/3