The simple harmonic oscillation of a particle are according to the equation x=5os(2pit+(pi)/4) metre. Find the (i) displacement (ii) velcoity and (iii) 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=5os(2pit+(pi)/4) metre. Find the (i) displacement (ii) velcoity and (iii) acceleration at t=0.
Answer» SOLUTION :Comparing with the general equation `x=A COS (omegat +phi_(0))` Amplitude `A=5m` and `omega=2pi` (i) Displacement `x=5 cos (2pit+(pi)/4)` metre when `t=0, x=x_(0)=5"cos"(pi)/4=5xx1/(sqrt(2))=3.54m` (ii) velocity `v=omega sqrt(A^(2)-x^(2))` when `t=0, v=v_(0)=omegasqrt(A^(2)-x_(0)^(2))` `=2pisqrt(5^(2)-(5/(sqrt(2)))^(2))=2pisqrt(25-25/2)` `=2pisqrt(25/2)=22.2ms^(-1)` (III) Acceleration `a=-omega^(2)x` when `t=0=a=a_(0)=-omega^(2)-omega^(2)x_(0)` `=-(2pi)^(2)3.54=-4pi^(2)(3.54)^(2)` `:.a_(0)=139.42ms^(-2)`