A body oscillates with SHM along with x - axis.
Its displacement varies with time according to the equation `x=(4.00m)cos(pi_(t)^(+)(pi)/(4))` calculate at t = 1.00s : (a) displacement (b) velocity (c) acceleration (d) Also calculate the maximum speed and maximum acceleration and (e) phase at t = 2.00s.

Explanation

By comparing the given equation with the general equation for SHM along x - axis,
`x=Acos(squaret+varphi)` , we get
`A=4.00m, square = piad//s, phi_(0)=pi/4`
Displacement at t = 1.00s,
`x=(4.00m)cos(pixx1+(pi)/(4))=(4.00)(-cos.(pi)/(4))`
`=(4.00)(-0.707)=-2.83m`
Velocity at `t=1.00s,v=-squareAsin(squaret+varphi_(0))`
`v=-((pi)/(s))(4.00m)sin[pixx1+(pi)/(4)]`
`=-(4.00pi)(-sin.(pi)/(4))ms^(-1)`
`=8.89m//s`
Acceleration :
`a=-square^(2)Acos (squaret+varphi_(0))`
`=-pi^(2)xx4.00cos(pixx1+m)`
`=-(4.00pi^(2))(-cos.(pi)/(4))ms^(-2)`
`=4.00xx(3.14)^(2)xx0.707ms^(-2)`
`=27.9ms^(2)`
Maximum Velocity , `a_("max")=square^(2)A=pi^(2)xx4.00`
`" "=39.5ms^(-2)`
Phase `(squaret+varphi_(0))=((pi)/(2))xx2s+pi/4=2pi+pi/4=(9pi)/4`