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A particle executing SHM oscillates be b...

A particle executing SHM oscillates be between two fixed points separated by `20 cm` . If its maximum velocity be `30 cm//s`. Find its velocity when its displacement is `5 cm` from its mean position.

Text Solution

Verified by Experts

Evidenty, the maximum displacement `= 20//2 = 10 cm` For a partical excuting SHM, the speed at a displacement 'x' is given by
`v = omega ssqrt(a^(2) - x^(2))` (i)
and `v_(max) = omega a` (ii)

Dividing Eq. (i) and (ii) by eq. (ii), we get `(v)/(v_(max)) = (a)/(sqrt(a^(2) - x^(2)))`
`implies (v)/(v_(max)) = (10)/(sqrt(10^(2) - 5^(2))) implies (10)/(5 sqrt 3) = (2sqrt 3)/(3)`
`v = 30 xx (2sqrt 3)/(3) = 20 sqrt3 em//s`
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