The phase difference between displacement and acceleration of a particle in a simple harmonic motion is:

Question

The phase difference between displacement and acceleration of a particle in a simple harmonic motion is: (A) π rad (B)  (3π/2) rad (C)  (π/2) rad (D) zero

Tardigrade Admin · Accepted Answer

Displacement of the particle executing SHM

x = A

sin wt Acceleration of the particle

a = \frac{d ^{2} x}{d t ^{2}}

⟹ a = - A w^{2} sin wt = A w^{2} sin (π + wt)

Thus phase difference between displacement and acceleration of the particle is

π

radian.

Q. The phase difference between displacement and acceleration of a particle in a simple harmonic motion is:

$π$ rad

$\frac{3 π}{2}$ rad

$\frac{π}{2}$ rad

$zero$

Displacement of the particle executing SHM $x = A$ sin wt Acceleration of the particle $a = \frac{d ^{2} x}{d t ^{2}}$
$⟹ a = - A w^{2} sin wt = A w^{2} sin (π + wt)$
Thus phase difference between displacement and acceleration of the particle is $π$ radian.

Q. The phase difference between displacement and acceleration of a particle in a simple harmonic motion is:

π rad

23π​ rad

2π​ rad

zero

Displacement of the particle executing SHM x=A sin wt Acceleration of the particle a=dt2d2x​ ⟹a=−Aw2sinwt=Aw2sin(π+wt) Thus phase difference between displacement and acceleration of the particle is π radian.

$π$ rad

$\frac{3 π}{2}$ rad

$\frac{π}{2}$ rad

$zero$

Displacement of the particle executing SHM $x = A$ sin wt Acceleration of the particle $a = \frac{d ^{2} x}{d t ^{2}}$
$⟹ a = - A w^{2} sin wt = A w^{2} sin (π + wt)$
Thus phase difference between displacement and acceleration of the particle is $π$ radian.