Question

At which point the acceleration of a particle executing SHM is maximum and what will be its value?
1. a_max = Aω² at mean position
2. amax = Aω2 at extreme position
3. amax = Aω at mean position
4. amax = Aω at extreme position

Answer 1

Correct Answer - Option 2 : amax = Aω2 at extreme position

CONCEPT:

• Simple harmonic motion occurs when the restoring force is directly proportional to the displacement from equilibrium.

F α -x

Where F = force and x = the displacement from equilibrium.

• For a simple harmonic motion equation of acceleration

\(\overrightarrow{a}=-ω^2\overrightarrow{x}\)

where a is the acceleration ω is the angular frequency and x is the displacement.

EXPLANATION:

The equation of displacement in SHM is given by:

x = A sinωt .........(i)

differentiate eq (i) with respect to time t

v = Aω cosωt

differentiate it with respect to time t

a = -Aω² sinωt

a = -ω2 A sinωt

a = -ω2 x

\(\overrightarrow{a}=-ω^2\overrightarrow{x}\)

the maximum value of a can be obtained for the maximum value of displacement x.

For SHM displacement is maximum at its extreme point i.e. x = A. So

amax = Aω²

And this maximum value is obtained at x = A or an extreme point.

So the correct answer is option 2.