MHT CET20225 Aug 2022Morning ShiftPhysicsOscillationsActual
If ' v ' is velocity and ' a ' is acceleration of a particle executing linear simple harmonic motion. Which one of the following statements is correct?
Options
- Awhen ' a ' is maximum, v is maximum
- Bwhen ' a ' is maximum, v is zero
- Cwhen ' a ' is zero, v is zero
- D' a ' is zero for any value of ' v '
Correct answer
B. when ' a ' is maximum, v is zero
Step-by-step solution
The correct option is (B). Concept: For SHM, a =- ( ^2 ) x is the necessary condition. A general solution for SHM can be written as, x=A ( t+ ) where, x is the displacement from mean position, A is the amplitude, is the angular frequency and is the phase angle. On taking the first derivative, velocity can be written as v= d x d t =(A ) ( t+f)=(A w) ( t+ + 2 ) And, taking derivative of velocity, acceleration can be written as: a = dv dt =- ( A ^2 ) ( t + )= ( A ^2 ) ( t + + ) Therefore, in SHM acceleration is ahead