A mass attached to a spring is free to oscillate, with angular velocity `omega`, in a horizontal plane without friction or damping. It is pulled to a distance `x_(0)` and pushed towards the centre with a velocity `v_(0)` at time `t=0`. Determine the amplitude of the resulting oscillations in terms of the parameters `omega, x_(0)and v_(0)`.

Explanation

To find the amplitude of the resulting oscillations of a mass attached to a spring, we can follow these steps:

### Step 1: Understand the Initial Conditions
At time \( t = 0 \):
- The mass is pulled to a distance \( x_0 \) from the equilibrium position.
- It is pushed towards the center with a velocity \( v_0 \).

### Step 2: Write the Equations of Motion
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