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A body oscillates with SHM according to ...

A body oscillates with SHM according to the equation (in SI units),
`x = 5 cos [2pi t + pi//4]`.
At t = 1.5 s, calculate the (a) displacement, (b) speed and (c) acceleration of the body.

Text Solution

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The angular frequency `omega` of the body `= 2pi s^(-1)` and its time period T = 1 s.
At t = 1.5 s
(a) displacement = (5.0 m) cos `[(2pis^(-1)xx1.5s+pi//4]`
`=(5.0 m) cos [(3pi + pi//4)]`
`=05.0xx0.707m`
`=-5.0xx0.707m`
`=3.535m`
(b) Using Eq. (14.9), the speed of the body
`=-(5.0m)(2pis^(-1))sin[(2pis^(-1))sin[(2pis^(-1))xx1.5s+pi//4]`
`=-(5.0m)(2pis^(-1))sin[(3pi+pi//4)]`
`=10pixx0.707ms^(-1)`
`=22ms^(-1)`
(c) Using Eq.(14.10), the acceleration of the body
`=-(2pis^(-1))^(2)xx` displacement
`=-(2pis^(-1))^(2)xx(-3.535m)`
`=140ms^(-2)`
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