Question

A particle performing SHM takes time equal to T (time period of SHM) in consecutive appearances at a particular point. The point is
A. An extreme position
B. The mean position
C. Between positive extreme and mean position
D. Between negative extreme and mean position

Answer 1

Hint: Define simple harmonic motion and think of how the particle moves, with respect to the equilibrium position. Define the time period for the motion, observe the path of the object for one time period and note down which position takes place only one.

Complete step-by-step answer:
SHM is an abbreviation for simple harmonic motion is a type of oscillating motion of an object. Some examples of SHM are mass attached to a spring, a pendulum, vibrations of molecules etc. It is the oscillation of the object around its state of equilibrium.
For a simple harmonic motion to occur, the resultant force acting on the object must be directly proportional to its displacement from its equilibrium point and it must always act towards the equilibrium point. Expressed in the following equation:
$F=-kx$
Where, F is the force on the object, k is a constant and x is the displacement from the point of equilibrium.
The time taken for the object covers a complete cycle of SHM that is, when the object returns to the point with the same velocity, is the time period T.
Now, at one extreme position, the object will return only after completing one cycle. Which means, it takes T time to return back to the extreme positions.
Therefore, the correct answer is option A.

Note: Other options are incorrect as the object takes those positions twice during one time period. For example, at the mean or equilibrium position, the object once travels in one direction, then again after half the time period, in the opposite direction. Similarly, at any other position, other than the extremes, the object returns twice in one time period.