A body oscillates with SHM according to the equation
`x(t)=5cos(2pit+pi//4)`
where t is in second and x in metres. Calculate (a) displacement at t=0 (b) time period (c) initial velocity

Explanation

`x(t)=5cos(2pit+pi//4)` …(i)
(a) At `t=0,`
displacement, `x(0)=5cos(2pixx0+pi//4)`
or `x(0)=5cospi//4=(5)/(sqrt(2))m`
(b) Comparing (i) with the standard equation of SHM.
`x(t)=Acos(omegat+phi_(0)),` we have
`omega=2pi or (2pi)/(T)=2pi or T=1s`
(c) Velocity, `upsilon=(dx)/(dt)`
`=[-5sin(2pit+pi//4)]xx2pi`
At `t=0,` initial velocity,
`upsilon_(0)=[-5sin(2pixx0+pi//4)]xx2pi`
`=(-10pi)/(sqrt(2))=-5sqrt(2)pims^(-1)`