1.

The displacement of a particle in S.H.M. varies according to the relationx = 4(cos pi t + sin pit) . The amplitude of the particle is

Answer»

`-4`
4
`4sqrt(2)`
8

Solution :`X = 4(cos PI t+ sin pit)`
`= 4sqrt(2) (1/sqrt(2) cos pit + 1/sqrt(2) sin pit)`
`=4sqrt(2) [sin pi/4 cos pi t + cos pi/4 sin pit]`
`=4sqrt(2) [sin pit cos pi/4 + cos pi t sin pi/4]`
`=4sqrt(2) sin (pi t + pi/4)`
HENCE, the AMPLITUDE of particle is `4sqrt(2)`.


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