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QAIPMT-2010-Ph-2050: NEET 2010 Physics - Class 11 AIPMT-2010-Ph-2050 Solution: The displacement of a particle along the x-axis is given by…
The displacement of a particle along the x-axis is given by . The motion of the particle corresponds to
Multiple Choice Options
- A simple harmonic motion of frequency
- B simple harmonic motion of frequency
- C non simple harmonic motion
- D simple harmonic motion of frequency
Step-by-Step Verified Solution
x = a sin 2 _ t = a ( 1 _ cos _ 2 _ t 2 )
( _ cos _ 2 _ = 1 _ 2 sin 2 _ )
= a 2 _ a cos _ 2 _ t 2
_ Velocity, v = d x d t = 2 _ a sin _ 2 _ t 2 = _ _ sin _ 2 _ t
Acceleration, a = d v d t = 2 _ 2 a cos _ 2 _ t
For the given displacement x = _ sin _ 2 _ t ,
a _ _ x is not satisfied.
Hence, the motion of the particle is non simple harmonic motion.
Note : The given motion is a periodic motion with a time period
T = 2 � 2 _ = � _