The position of a particle with respect to origin varies according to the relation x=3 sin 100 t+8 cos 2 50 t. The maximum displacement of the particle from the origin is

Question

The position of a particle with respect to origin varies according to the relation x=3 sin 100 t+8 cos 2 50 t. The maximum displacement of the particle from the origin is  (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 100 t]/2) x=4+3 sin 100 t+4 cos 100 t (x-4)=5 sin (100 t+φ) tan φ=(4/3) Amplitude =5 units Maximum displacement =9 units

Q. The position of a particle with respect to origin varies according to the relation $x = 3 sin 100 t + 8 cos^{2} 50 t$ . The maximum displacement of the particle from the origin is ____

$x = 3 sin 100 t + 8 cos^{2} 50 t$
$= 3 sin 100 t + \frac{8 [ 1 + c o s 100 t ]}{2}$
$x = 4 + 3 sin 100 t + 4 cos 100 t$
$(x - 4) = 5 sin (100 t + ϕ) {tan ϕ = \frac{4}{3}}$
Amplitude $= 5$ units
Maximum displacement $= 9$ units

Q. The position of a particle with respect to origin varies according to the relation x=3sin100t+8cos250t. The maximum displacement of the particle from the origin is ____

x=3sin100t+8cos250t =3sin100t+28[1+cos100t]​ x=4+3sin100t+4cos100t (x−4)=5sin(100t+ϕ){tanϕ=34​} Amplitude =5 units Maximum displacement =9 units

Q. The position of a particle with respect to origin varies according to the relation $x = 3 sin 100 t + 8 cos^{2} 50 t$ . The maximum displacement of the particle from the origin is ____

$x = 3 sin 100 t + 8 cos^{2} 50 t$
$= 3 sin 100 t + \frac{8 [ 1 + c o s 100 t ]}{2}$
$x = 4 + 3 sin 100 t + 4 cos 100 t$
$(x - 4) = 5 sin (100 t + ϕ) {tan ϕ = \frac{4}{3}}$
Amplitude $= 5$ units
Maximum displacement $= 9$ units