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Mechanical Properties Of Fluids

Question
CBSEENPH11019098

What type of force is necessary for the particle to execute simple harmonic motion?

Solution
A particle executing simple harmonic motion has acceleration directly proportional to displacement and is directed towards the mean position.
Mathematically, we can write, 
 space space space space space space space space space space space space space space space straight alpha proportional to negative straight y

U s i n g space N e w t o n apostrophe s space f i r s t space L a w space o f space m o t i o n comma space

space space space space space space space space space space space space space space space space space space straight F equals m a

therefore space space space space space space space space space space space space straight F space proportional to negative m y space

rightwards double arrow space space space space space space space space space space space space space straight F space proportional to negative straight y 

Therefore, the force required to execute simple harmonic motion is directly proportional to displacement and directed towards the mean position.
The force directed towards mean position is called restoring force.
Thus a restoring force is directly proportional to displacement and is necessary for the particle to execute simple harmonic motion.