Rankers Physics
Topic: Oscillation
Subtopic: Equation of SHM

A particle is in linear SHM between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction, find the signs of velocity, acceleration and force on the particle when it is 4 cm from B going towards A :
+, –, +
–, +, –
–, –, –
+, +, +

Solution:

For a particle in simple harmonic motion (SHM), the force and acceleration are always directed towards the equilibrium position (center) and are opposite to the displacement.

Solution:

1. Displacement: Since the particle is 4 cm from \( B \) and moving towards \( A \), it is located closer to \( B \) on the negative side of the equilibrium point. This means the displacement is in the negative direction.

2. Velocity: Since the particle is moving towards \( A \) (the negative direction), its velocity is negative.

3. Acceleration and Force: In SHM, acceleration and force are always directed towards the equilibrium point. Since the particle is on the positive side of the equilibrium (closer to \( B \)), the acceleration and force are in the negative direction.

Conclusion:
The signs of velocity, acceleration, and force are all negative (–, –, –).

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