SHM given by `x= 6 sin omega t + 8 cos omega t ` . Its amplitude is

Options

A. 10 cm
B. 2 cm
C. 14 cm
D. 3.5 cm

Answer

A

Explanation

A harmonic oscillation of constant amplitude and of single frequency is called simple harmonic oscillation.
Here, `x = 8 sin omega t + 6 cos omega t`
`a_(1) = 8 cm and a_(2) = 6 cm`
`therefore` Amplitude of motion, `A = sqrt(a_(1)^(2)+a_(2)^(2))=sqrt(8^(2)+6^(2))`
`= sqrt(64 + 36) = sqrt(100) = 10` cm