Question

The displacement of a particle executing simple harmonic motion is given by y = A₀ + A sinωt + B cosωt.
Then the amplitude of its oscillation is given by :
(1) A₀ + √(A² + B²)
(2) √(A² + B²)
(3) √{A²₀ + (A + B)²}
(4) A + B

Answer 1

The amplitude of its oscillation is given by

$\bold{\sqrt{A^{2}+B^{2}}}$

Step by step explanation:

"Simple harmonic motion in which restoring force is directly proportional to the displacement of the particle from the mean or equilibrium position."

From the given,

The displacement of a particle executing simple harmonic motion is given by

$\bold{y=A_{o}+A\,sin\omega t+B\,cos\omega t}$

$y^{I}=y-A_{o}$

$\Rightarrow A\,sin\,\omega t+B\,cos\,\omega t$

From the diagram, (in attachment)

$R=\sqrt{A^{2}+B^{2}+2AB\,cos\,90^{o}}$

 $\Rightarrow \sqrt{A^{2}+B^{2}}$

The amplitude of its oscillation is given by $\bold{\sqrt{A^{2}+B^{2}}}$.