The displacement of a particle is given at time t, by x=A sin (-2 ω t)+B sin 2 ω t Then

Question

The displacement of a particle is given at time t, by x=A sin (-2 ω t)+B sin 2 ω t Then (A) the motion of the particle is SHM with an amplitude of √A2+(B2/4) (B) the motion of the particle is not SHM, but oscillatory with a time period of T = π ω (C) the motion of the particle is oscillatory with a time period of T = π 2ω (D) the motion of the particle is a periodic.

Tardigrade Admin · Accepted Answer

The displacement of the particle is given by

x = A sin (- 2 ω t) + B sin^{2} ω t

= - A sin 2 ω t + \frac{B}{2} (1 - cos 2 ω t)

= - (A sin 2 ω t + \frac{B}{2} cos 2 ω t) + \frac{B}{2}

This motion represents

S H M

with an amplitude

A^{2} + \frac{B}{4}

and mean position

\frac{B}{2}

.

Q. The displacement of a particle is given at time $t$ , by $x = A sin (- 2 ω t) + B sin^{2} ω t$ Then

the motion of the particle is SHM with an amplitude of $A^{2} + \frac{B ^{2}}{4}$

the motion of the particle is not SHM, but oscillatory with a time period of $T = πω$

the motion of the particle is oscillatory with a time period of $T = π 2 ω$

the motion of the particle is a periodic.

The displacement of the particle is given by
$x = A sin (- 2 ω t) + B sin^{2} ω t$
$= - A sin 2 ω t + \frac{B}{2} (1 - cos 2 ω t)$
$= - (A sin 2 ω t + \frac{B}{2} cos 2 ω t) + \frac{B}{2}$
This motion represents $S H M$ with an amplitude
$A^{2} + \frac{B}{4}$ and mean position
$\frac{B}{2}$ .

Q. The displacement of a particle is given at time t, by x=Asin(−2ωt)+Bsin2ωt Then

the motion of the particle is SHM with an amplitude of A2+4B2​​

the motion of the particle is not SHM, but oscillatory with a time period of T=πω

the motion of the particle is oscillatory with a time period of T=π2ω