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

Question

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 (A) ω  (B) 2ω  (C) 4ω  (D) (ω /2)

Tardigrade Admin · Accepted Answer

x=sin2 ω t - 2 cos2 â¡ ω t =1-3cos2 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 2ω .

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

$ω$

$2 ω$

$4 ω$

$\frac{ω}{2}$

$x = s i n^{2} ω t - 2 co s^{2} ω t$
$= 1 - 3 co s^{2} ω t$
$= 1 - 3 (\frac{1 + cos 2 ω t}{2})$
$= - \frac{1}{2} - \frac{3}{2} cos 2 ω t$
Which is a periodic function with angular frequency of $2 ω$ .

Q. A simple harmonic motion is represented by x(t)=(sin)2ωt−2(cos)2⁡ωt . The angular frequency of oscillation is given by

ω

2ω

4ω

2ω​

x=sin2ωt−2cos2⁡ωt =1−3cos2ωt =1−3(21+cos2ωt​) =−21​−23​cos2ωt Which is a periodic function with angular frequency of 2ω .

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

$ω$

$2 ω$

$4 ω$

$\frac{ω}{2}$

$x = s i n^{2} ω t - 2 co s^{2} ω t$
$= 1 - 3 co s^{2} ω t$
$= 1 - 3 (\frac{1 + cos 2 ω t}{2})$
$= - \frac{1}{2} - \frac{3}{2} cos 2 ω t$
Which is a periodic function with angular frequency of $2 ω$ .