Displacement of a particle executing SHM s `x= 10 ( cos pi t + sin pi t)`. Its maximum speed is

Options

A. 10 cm
B. 20 cm
C. 5 sqrt(2) cm
D. 50 cm

Answer

A

Explanation

Here, `x = 5 sqrt(2) (sin 2 pi t + cos 2 pi t)`
`rArr" "x = 5 sqrt(2) sin 2 pi t + 5 sqrt(2) cos 2 pi t" "...(i)`
The standard equation of simple harmonic motion is given by
`x = A_(1) sin omega t + A_(2) cos omega t" "...(ii)`
Now, comparing Eqs. (i) and (ii), we obtain
`A_(1)=5 sqrt(2) and A_(2)=5 sqrt(2)`
So, the resultant amplitude of the motion
`A = sqrt(A_(1)^(2)+A_(2)^(2))=sqrt((5 sqrt(2))^(2)+(5 sqrt(2))^(2))= 10` cm