A body oscillates with SHM, accroding to the equation, `x=(5.0m)cos[(2pirads^(-1))t+pi//4]`
At `t=1.5s`, calculate the `(a)` diplacement `(b)` speed and `(c)` acceleration of the body.

Explanation

The angular frequency `omega` of the body `= 2pis^(-1)` and its time period `T = 1s`
At `t=1.5s`
(a) displacement `= (5.0 m) cos [(2 pi s^(-1))xx1.5 s +pi//4]`
`=(5.0 m) cos [(3pi + pi//4)]`
`= -5.0 xx 0.707 m`
`=-2.535` m
(b) Using Eq. (14.9), the speed of the body
`= -(5.0 m)(2pi s^(-1))sin [(2pi s^(-1))xx1.5 s + pi//4]`
`=-(5.0 m)(2pi s^(-1))sin [(3pi +pi//4)]`
`=10 pi xx 0.707 ms^(-1)`
`=22 ms^(-1)`
(c) Using Eq. (14.10), the acceleration of the body
`= (2pi s^(-1))^(2) xx` displacement
`= -(2pi s^(-1))^(2) xx (-3.535m)`
`= 140 ms^(-2)`.