2004 AIPMT OscillationsVelocity and Acceleration in SHM Easy Question 2 of 2 in Velocity and Acceleration in SHM

Which one of the following statements is true for the speed 'v' and the acceleration 'a' of a particle executing simple harmonic motion

A Value of a is zero, whatever may be the value of 'v'
B When 'v' is zero, a is zero
C When 'v' is maximum, a is zero
D When 'v' is maximum, a is maximum

The answer is C.

Solution

For SHM $x = A\sin\omega t$:
Velocity: $v = \omega\sqrt{A^2 - x^2}$
Acceleration: $a = -\omega^2 x$
At the mean position ($x = 0$): $v = v_{max} = A\omega$ and $a = 0$.
At the extreme positions ($x = \pm A$): $v = 0$ and $a = a_{max} = \omega^2 A$.
So in SHM, if $v = v_{max}$ then $a = 0$, and if $v = 0$ then $a = a_{max}$.
The true statement is: when 'v' is maximum, a is zero.

Concept Velocity and acceleration at mean and extreme positions

Velocity and Acceleration in SHM in past papers

2 questions from this chapter have appeared across 2 exam years.