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CBSE Class 11-science Answered

Derive the expression
A=root(a^2+b^2)
where A is amblitude.
Asked by Vineeth K | 07 Feb, 2015, 05:12: PM
answered-by-expert Expert Answer
Sine and cosine functions are periodic functions, and hence, a particle performing a periodic motion will return to its initial position after one time period.
 
The linear combination of sine and cosine function is also periodic in nature.
 
Consider a combination of these two fucntions as,
 
begin mathsize 12px style straight x equals straight f left parenthesis straight t right parenthesis space equals space straight a space sin space ωt space plus space straight b space cos space ωt Taking space straight a space equals space straight A space cos space straight ϕ space and space straight b space equals space straight A space sin space straight ϕ comma space we space get straight x space equals space straight A space cos space ϕsin space ωt space plus space Asinϕ space cos space ωt space equals space straight A space sin space open parentheses ωt space plus space straight ϕ close parentheses Now comma space straight a squared equals straight A squared cos squared straight ϕ space and space straight b squared equals straight A squared sin squared straight ϕ Adding space the space above space two space equations comma space we space get straight a squared plus straight b squared equals straight A squared open parentheses cos squared straight ϕ plus sin squared straight ϕ close parentheses equals straight A squared therefore straight A equals square root of straight a squared plus straight b squared end root end style
Answered by Romal Bhansali | 09 Feb, 2015, 11:27: AM

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CBSE 11-science - Physics
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