`x_(1) = 5 sin omega t`
` x_(2) = 5 sin (omega t + 53^(@))`
`x_(3) = - 10 cos omega t`
Find amplitude of resultant SHM.

Explanation

To find the amplitude of the resultant simple harmonic motion (SHM) given the equations \( x_1 = 5 \sin(\omega t) \), \( x_2 = 5 \sin(\omega t + 53^\circ) \), and \( x_3 = -10 \cos(\omega t) \), we will follow these steps:

### Step 1: Convert all equations to sine form
We can express \( x_3 \) in terms of sine to make it easier to combine the equations. We know that:
\[ \cos(\theta) = \sin\left(\theta + 90^\circ\right) \]
Thus, we can rewrite \( x_3 \):
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