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.

A body oscillates with SHM according to the equation (in SI units), x

1.	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.
Answer» Solution :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)`