The simple harmonic oscillation of a particle are according to the equation x= 5cos(2pit+ (pi)/(4)) meter. Find the(i) displacement, (ii) velocity and (ii) acceleration at t = 0.

The simple harmonic oscillation of a particle are according to the equ

1.	The simple harmonic oscillation of a particle are according to the equation x= 5cos(2pit+ (pi)/(4)) meter. Find the(i) displacement, (ii) velocity and (ii) acceleration at t = 0.
Answer» SOLUTION :Comparing with, the general equation `x= Acos(omegat+phi_(0))` Amplitude A= 5M and `OMEGA= 2pi` i) Displacement `x= 5cos(2pit+(pi)/(4))` meter when `t=0 , x= x_(0)= 5cos((pi)/(4))= 5 xx (1)/(sqrt(2))= 3.54m` ii) velocity `v= omegasqrt(A^(2)-x^(2))` when `t=0 , v= v_(0)= omegasqrt((A^(2)-x^(2))` `= 2pisqrt(5^(2)- ((5)/(sqrt(2)))^(2))= 2pisqrt(25-(25)/(2))` `= 2pisqrt((25)/(2))= 22.2 ms^(-1)` iii) Acceleration `a= -omega^(2)x` when `t=0 = a= a_(0)= -omega^(2)x_(0)` `= -(2pi)^(2)3.54= -4pi^(2)(3.54)^(2)` `:. a_(0)= 139.42 ms^(-2)`