The displacement equation of a particle is x=3 sin 2t+4 cos 2t, where x is in metre and t in second. The amplitude and maximum velocity will be respectively:

Question

The displacement equation of a particle is x=3 sin 2t+4 cos 2t, where x is in metre and t in second. The amplitude and maximum velocity will be respectively: (A) 5m, 10 m/s (B) 3m, 2 m/s (C) 4m, 2 m/s (D) 3m, 4 m/s

Tardigrade Admin · Accepted Answer

Displacement equation is x=3 sin 2 t+4 cos 2 t Comparing this equation with x=a1 sin ω t+a2 cos ω t We get, a1=3, a2=4, ω=2 ∴ a=√a12+a22 =√32+42=5 metre and maximum velocity v max =a ω=5 × 2=10 m / s

Q. The displacement equation of a particle is $x = 3 sin 2 t + 4 cos 2 t,$ where $x$ is in metre and t in second. The amplitude and maximum velocity will be respectively:

5m, 10 m/s

3m, 2 m/s

4m, 2 m/s

3m, 4 m/s

Displacement equation is
$x = 3 sin 2 t + 4 cos 2 t$
Comparing this equation with
$x = a_{1} sin ω t + a_{2} cos ω t$
We get,
$a_{1} = 3, a_{2} = 4, ω = 2$
$∴ a = a_{1}^{2} + a_{2}^{2}$
$= 3^{2} + 4^{2} = 5$ metre
and maximum velocity
$v_{m a x} = aω = 5 \times 2 = 10 m / s$

Q. The displacement equation of a particle is x=3sin2t+4cos2t, where x is in metre and t in second. The amplitude and maximum velocity will be respectively: