Simple Harmonic Motion

For SHM
where a is acceleration, is angular velocity, is displacement. Hence, it is clear that acceleration is directly proportional to displacement and is always opposite to displacement.

Step 1: Understanding the Statement
The statement is true because, in a damped oscillating pendulum, the amplitude decreases over time due to energy loss (typically due to friction or air resistance).
This results in the pendulum coming to rest eventually.
Step 2: Understanding the Reason
The reason provided is incorrect.
The frequency of an oscillating pendulum remains constant during the damped motion (for small damping), even though the amplitude decreases.
In fact, the frequency of a damped pendulum changes only when damping is significant enough to alter the time period.
Step 3: Conclusion Thus, the statement is true, but the reason is false.

Step 1: Understand the concept of SHM.
In Simple Harmonic Motion (SHM), the displacement of the particle is given by: where is the amplitude, is the angular frequency, is the time, and is the phase constant.
Step 2: Given conditions.
At , the particle is at the centre, so .
The particle is initially moving towards the left, which means the velocity is negative.

Step 3: Velocity in SHM.
The velocity in SHM is given by: Since the particle starts at the centre and moves to the left, the phase constant is .
So, the displacement and velocity equations become:
Step 4: Find the position and velocity at . At , the angular position is: So, the particle is at the centre.
Step 5: Find the velocity. The velocity at is: Thus, the particle is moving with maximum speed towards the left.