Question

The average acceleration in one time period in a simple harmonic motion is
(a) Aω2
(b) Aω2/2
(c) Aω2/√2
(d) zero

Answer 1

The average acceleration in one time period in a simple harmonic motion is $\mathbf{\frac{A\omega ^{2}}{2}}$. Option B is correct.

Explanation:

1. During simple harmonic motion

   Amplitude of vibration = A

   Angular frequency of vibration=ω

2.

 Maximum value of acceleration at mean position $\mathbf{(a_{max})=A\omega ^{2}}$    ...1)

   

  Minimum value of acceleration at extreme position $\mathbf{(a_{min})=0}$     ...2)

3. Average value of acceleration $\mathbf{(a_{avg})=\frac{a_{max}+a_{min}}{2}}$        ...3)

   From equation 1) ,equation 2) and equation 3)

   Average value of acceleration$\mathbf{(a_{avg})=\frac{A\omega ^{2}+0}{2}}$

   

   Average value of acceleration$\mathbf{(a_{avg})=\frac{A\omega ^{2}}{2}}$

Answer 2

In a simple harmonic motion, in one time period, the average acceleration is  zero.

Explanation:

• The direction will be opposite when there is a change in the acceleration after each half oscillation. So, the net acceleration is shown as, $\left(-A \omega^{2}\right)+A \omega^{2}=0$.
• This question can be seen in a couple of ways:  
• (1) Net Acceleration = NET FORCE : MASS of the object. This is as shown by the second Newton’s law. so, NET FORCE = $m \times a$.
• (2) NET ACCELERATION is the VECTOR that is accelerations’ sum.