In a linear Simple Harmonic Motion (SHM):
(A) Restoring force is directly proportional to the displacement.
(B) The acceleration and displacement are opposite in direction.
(C) The velocity is maximum at mean position.
(D) The acceleration is minimum at extreme points.
Choose the correct answer from the options given below:
(A), (B) and (C) only
(C) and (D) only
(A), (C) and (D) only
(A), (B) and (D) only
Correct answer:A
Standard Method
Given: Statements about linear SHM are to be checked.
Find: Which combination of statements is correct.
Step 1: Analyze statement (A).
In linear SHM, the restoring force is given by which shows that the restoring force is directly proportional to the displacement from the mean position. Hence, statement (A) is correct.
Step 2: Analyze statement (B).
Acceleration in SHM is given by . This indicates that acceleration is always directed opposite to the displacement. Hence, statement (B) is correct.
Step 3: Analyze statement (C).
In SHM, the velocity is maximum at the mean position and zero at the extreme positions. Hence, statement (C) is correct.
Step 4: Analyze statement (D).
Acceleration is maximum at the extreme positions and zero at the mean position. Thus, statement (D) is incorrect.
Step 5: Final conclusion.
Only statements (A), (B) and (C) are correct. Therefore, the correct option is A.
Quick Concept Check
Given: Basic properties of SHM.
Find: The correct set of statements.
Use the standard SHM facts: restoring force and acceleration always act towards the mean position, velocity is maximum at mean position, and acceleration is maximum at extreme positions.
So, (A), (B), and (C) are correct while (D) is false. Therefore, the correct option is A.
Confusing proportionality with direction in . The minus sign shows direction opposite to displacement, while proportionality is with the magnitude of displacement. Treat statement (A) as correct.
Assuming acceleration is minimum at the extreme points because the particle stops there. In fact, velocity is zero at extremes, but acceleration magnitude is maximum there. Distinguish velocity from acceleration.
Thinking velocity and acceleration behave the same way at the mean position. In SHM, velocity is maximum at the mean position, but acceleration is zero there. Use separate SHM relations for each quantity.
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