The displacement of a particle varies according to the relation x=3 sin 100 t+8 cos 2 50 t. The amplitude of the resultant SHM is y units. Find y.

Question

The displacement of a particle varies according to the relation x=3 sin 100 t+8 cos 2 50 t. The amplitude of the resultant SHM is y units. Find y. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

x=3 sin 100 t+8 cos 2 50 t =3 sin 100 t+8((1+ cos 2 × 50 t/2)) =3 sin 100 t+4 cos 100 t+4 x=5 sin (100 t)+4 ⇒ A=5

Q. The displacement of a particle varies according to the relation $x = 3 sin 100 t + 8 cos^{2} 50 t$ . The amplitude of the resultant SHM is $y$ units. Find $y$ .

$x = 3 sin 100 t + 8 cos^{2} 50 t$
$= 3 sin 100 t + 8 (\frac{1 + c o s 2 \times 50 t}{2})$
$= 3 sin 100 t + 4 cos 100 t + 4$
$x = 5 sin (100 t) + 4$
$\Rightarrow A = 5$

Q. The displacement of a particle varies according to the relation x=3sin100t+8cos250t. The amplitude of the resultant SHM is y units. Find y.

x=3sin100t+8cos250t =3sin100t+8(21+cos2×50t​) =3sin100t+4cos100t+4 x=5sin(100t)+4 ⇒A=5

Q. The displacement of a particle varies according to the relation $x = 3 sin 100 t + 8 cos^{2} 50 t$ . The amplitude of the resultant SHM is $y$ units. Find $y$ .

$x = 3 sin 100 t + 8 cos^{2} 50 t$
$= 3 sin 100 t + 8 (\frac{1 + c o s 2 \times 50 t}{2})$
$= 3 sin 100 t + 4 cos 100 t + 4$
$x = 5 sin (100 t) + 4$
$\Rightarrow A = 5$