Question

The SHM of a particle is given by the equation x= 2 sin wt + 4 cos wt. it's amplitude of oscillation is

1. 4 2. 2 3.6 4.2 root 5

Answer 1

Answer: (4). The amplitude of oscillation is $a = 2\sqrt5$

Explanation:

Given that,

The equation is

$x = 2\ sin\omega t + 4 cos \omega t$

We know the general equation is

$x = A\ sin\omega t + B\ cos\omega t$

Now, the amplitude of oscillation is

$a = \sqrt{A^{2} + B^{2}}$....(I)

Where, A = 2 and B = 4

Put the value of A and B in equation (I)

$a = \sqrt{2^{2} + 4^{2}}$

$a = 2\sqrt5$

Hence, the amplitude of oscillation is $a = 2\sqrt5$