A ball of mass m kept at the centre of a string of length `L` is pulled from centre in perpendicular direction and released. Prove that motion of ball is simple harmonic and determine time period of oscillation
A ball of mass m kept at the centre of a string of length `L` is pulled from centre in perpendicular direction and released. Prove that motion of ball is simple harmonic and determine time period of oscillation
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To solve the problem of proving that the motion of a ball attached to a string is simple harmonic motion (SHM) and determining the time period of oscillation, we can follow these steps:
### Step 1: Understand the Setup
We have a ball of mass \( m \) attached to a string of length \( L \). When the ball is pulled perpendicularly from the center and released, it will oscillate about the equilibrium position.
### Step 2: Analyze the Forces
When the ball is displaced by a distance \( x \) from the equilibrium position, the tension in the string \( T \) will create a restoring force. The components of the tension that act to restore the ball to its equilibrium position can be analyzed.
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