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.

Explanation

Comparing equation `x= 5cos [2pi t+(pi)/(4)]` with general equation of SHM
Amplitude A= 5 unit
`omega = 2pi rad s^(-1), T= 1s`.
Velocity `v(t) = A omega sin (omega t+ phi)`
`= -5xx (2pi)sin(2pixx1.5+(pi)/(4))`
`= -10pi sin (3pi+(pi)/(4)) " "[therefore sin(3pi+ theta)= -sin theta]`
`= +10pi xx (1)/(sqrt(2)) = +(10xx 3.14)/(1.414)`
`therefore v(t) = +22.2 ms^(-1)`.