The displacement of a particle executing simple harmonic motion is given by y =A0+ A sin wt + B cos wt Then the amplitude of its oscillation is given by:

Question

The displacement of a particle executing simple harmonic motion is given by y =A0+ A sin wt + B cos wt Then the amplitude of its oscillation is given by: (A) √ A20 +(A+B)2 (B) A+B (C) A0 +√A2+B2 (D) √A2+B2

Tardigrade Admin · Accepted Answer

x=A0+A sin wt+B cos w t x-A0=A sin wt+B cos w t ∴ Amplitude =√A2+B2+2 A B cos 90 =√A2+B2

Q. The displacement of a particle executing simple harmonic motion is given by $y = A_{0} + A s in wt + B cos wt$
Then the amplitude of its oscillation is given by:

$A_{0}^{2} + (A + B)^{2}$

$A + B$

$A_{0} + A^{2} + B^{2}$

$A^{2} + B^{2}$

$x = A_{0} + A sin wt + B cos wt$
$x - A_{0} = A sin wt + B cos wt$
$∴$ Amplitude $= A^{2} + B^{2} + 2 A B cos 90$
$= A^{2} + B^{2}$

Q. The displacement of a particle executing simple harmonic motion is given by y=A0​+Asinwt+Bcoswt Then the amplitude of its oscillation is given by:

A02​+(A+B)2​

A+B

A0​+A2+B2​

A2+B2​