If a freely suspended object is pulled to one side and released, it oscillates about the point of suspension because the
acceleration is directly proportional to the displacement
motion is directed away from the equilibrium point
acceleration is directly proportional to the square of the displacement
velocity is minimum at the equilibrium ponit
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The correct answer is:
**A. acceleration is directly proportional to the displacement** 
### **Explanation:**
When a freely suspended object is pulled to one side and released, it performs **simple harmonic motion (SHM)**. In SHM:
- The **restoring force** that brings the object back towards the equilibrium point is directly proportional to the displacement from that point and acts **in the opposite direction**.
- According to Newton's second law, since force is proportional to acceleration (\( F = ma \)), this also means that **acceleration is directly proportional to displacement** and directed towards the equilibrium point.
Mathematically, this is expressed as:
\[
a = -\omega^2 x
\]
Where:
- \( a \) = acceleration
- \( x \) = displacement from the equilibrium point
- \( \omega \) = angular frequency
- The negative sign indicates that the acceleration is directed **towards** the equilibrium point.
Therefore, **A. acceleration is directly proportional to the displacement** is the correct answer. 
C. acceleration is directly proportional to the square of the displacement.
When a freely suspended object (such as a pendulum) is pulled to one side and released, it undergoes simple harmonic motion (SHM) about the point of suspension. In simple harmonic motion, the restoring force acting on the object is directly proportional to its displacement from the equilibrium position and in the opposite direction of the displacement.
The equation of motion for simple harmonic motion is:
a = -ω^2 * x
where:
a = acceleration of the object,
ω (omega) = angular frequency of the oscillation, and
x = displacement of the object from the equilibrium position.
From the equation, we can see that the acceleration (a) is directly proportional to the square of the displacement (x^2) and is in the opposite direction of the displacement. This relationship is what allows the object to oscillate back and forth about the point of suspension. Option C correctly describes this relationship between acceleration and displacement in simple harmonic motion.
