Three sinusoidal displacements are applied in X-direction to a point mass in such a way that total displacement is zero and the mass comes to rest. What are the values of B and `phi` if the equations are
`x_(1) (t) = A sin 2 omega t`
`x_(2) (t) = A sin (2 omega t + (4pi)/(3))`
`x_(3) (t) = B sin (2 omega t + phi)`

Explanation

To solve the problem, we need to find the values of \( B \) and \( \phi \) such that the total displacement of the point mass due to the three sinusoidal displacements is zero. The equations of the displacements are given as follows:

1. \( x_1(t) = A \sin(2 \omega t) \)
2. \( x_2(t) = A \sin(2 \omega t + \frac{4\pi}{3}) \)
3. \( x_3(t) = B \sin(2 \omega t + \phi) \)

### Step 1: Write the total displacement equation
The total displacement \( x(t) \) is the sum of the three displacements:
...