Question 312: Oscillations

Question

A body is performing S.H.M. of amplitude 'A'. The displacement of the body from a point where kinetic energy is maximum to a point where potential energy is maximum, is

Accepted Answer

The correct answer is
Option B:  $$ \pm A $$
.
Here's why:
In Simple Harmonic Motion (SHM), the total mechanical energy (the sum of kinetic and potential energy) remains constant.  This means that when kinetic energy is at its maximum, potential energy is at its minimum, and vice-versa.
Let's break down the key points:
Kinetic Energy Maximum:
This occurs when the body is passing through its equilibrium position.  At this point, the velocity is maximum, and therefore kinetic energy is maximum.
Potential Energy Maximum:
This occurs at the extreme ends of the motion, where the body momentarily comes to rest.  At these points, the displacement from equilibrium is maximum, and hence potential energy is maximum.
Displacement:
The displacement from the point of maximum kinetic energy (equilibrium) to the point of maximum potential energy (extreme position) is exactly equal to the amplitude 'A'.
Therefore, the displacement is
$$ \pm A $$
(positive or negative depending on the direction of the motion).

Answer

zero

Answer

$$\pm \mathrm{A}$$

Answer

$$\pm \frac{\mathrm{A}}{2}$$

Answer

$$\pm \frac{\mathrm{A}}{4}$$

Oscillations

A body is performing S.H.M. of amplitude 'A'. The displacement of the body from a point where kinetic energy is maximum to a point where potential energy is maximum, is

Choose the correct answer: