A particle executes simple harmonic motion between x = -A and x = +A . If time taken by particle to go from x = 0 to A/2 is 2s; then time taken by particle in going from x = A/2 to A is 

Explanation:

In SHM, the motion can be represented as the projection of uniform circular motion. The time period T is the time for one complete oscillation. The motion from x = 0 to x = A corresponds to a quarter of the time period, or T/4.

Calculating the Time Period

• The time from x = 0 to x = A/2 is given as 2 seconds.
• This segment of motion corresponds to an angle of π/6 radians in the circular motion analogy, which is 1/12 of the full cycle.
• Thus, the total time period T can be calculated as: T = 2 seconds × 12 = 24 seconds

Time from x = A/2 to x = A

• The motion from x = A/2 to x = A corresponds to the segment between π/6 radians and π/2 radians, which is π/3 radians.
• This segment is 1/6 of the full cycle.
• Therefore, the time taken for this segment is: Time = T/6 = 24 seconds / 6 = 4 seconds

Final Answer

The time taken by the particle to move from x = A/2 to x = A is 4 seconds.