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The equation of an SHM is x=8 si...

The equation of an `SHM ` is x=8 ` sin omega t + 15 cos omega t , ` where x is displacement and t is time . The amplitude will be

A

23

B

7

C

10

D

17

Text Solution

Verified by Experts

`x= 8 sin omega + 15 cos omega t `
`= 17 [ sin omega t. (8 ) /( 17) + cos omega t. (15) /( 17 ) ]`
` [ :. 8^(2) + 15 ^(2)= 289 = 17 ^(2)]`
` = 17 [ sin omega t cos theta + cos omega t sin theta ]`
` [ " since" , theta cos ^(-1) (8) /( 17 ) = sin ^(-1) ( 15) /( 17 ) ] `
`=17 sin ( omega t+0 ) `
` therefore ` amplitude `= 17` unit
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