A simple harmonic motion is represented by x(t) = sin2 ω t - 2 cos2 ω t . The angular frequency of oscillation is given by

Question

A simple harmonic motion is represented by x(t) = sin2 ω t - 2 cos2 ω t . The angular frequency of oscillation is given by (A) ω (B) 2 ω (C)  4 ω (D) ω / 2

Tardigrade Admin · Accepted Answer

x= sin 2 ω t -2 cos 2 ω t =1-3 cos 2 ω t =1-3((1+ cos 2 ω t/2)) =-(1/2)-(3/2) cos 2 ω t which is a periodic function with angular frequency of 2 ω.

Q. A simple harmonic motion is represented by $x (t) = sin^{2} ω t - 2 cos^{2} ω t$ . The angular frequency of oscillation is given by

$ω$

$2 ω$

$4 ω$

$ω /2$

$ω /4$

$x = sin^{2} ω t - 2 cos^{2} ω t$
$= 1 - 3 cos^{2} ω t$
$= 1 - 3 (\frac{1 + c o s 2 ω t}{2})$
$= - \frac{1}{2} - \frac{3}{2} cos 2 ω t$
which is a periodic function with angular frequency of $2 ω$ .

Q. A simple harmonic motion is represented by x(t)=sin2ωt−2cos2ωt . The angular frequency of oscillation is given by

ω

2ω

4ω

ω/2

ω/4

x=sin2ωt−2cos2ωt =1−3cos2ωt =1−3(21+cos2ωt​) =−21​−23​cos2ωt which is a periodic function with angular frequency of 2ω.