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A particle is subjected to two simple ha...

A particle is subjected to two simple harmonic motions.
`x_(1) = 4.0 sin (100pi t)` and `x_(2) = 3.0 sin(100pi t + (pi)/(3))`
Find
(a) the displacement at `t = 0`
(b) the maximum speed of the particle and
(c ) the maximum acceleration of the particle.

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
`A_(R) = sqrt((4)^(2) + (3)^(2) + 2(4) (3)cos 60^(@)`

`= 6.1 units`
`tan phi = (3 sin 60^(@))/(4 + 3 cos 60^(@)) = 0.472`
`:. phi = 25.3^(@)`
`:. x = 6.1 sin (100 pi t + 25.3^(@))`
(a) At `t = 0`, `x = 6.1 sin 25.3^(@)`
`= 2.6 unit`
(b) `v_(max) = omega A`
`= (100 pi)(6.1)`
`= 1917 unit`
(c) `a_(max) = omega^(2) A`
`= (100 pi)^(2)(6.1)`
` = 6.0 xx 10^(5)` units.
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