Question

In shm, velocity is maximum at,
A) at extreme position
B) at central position
C) constant
D) none

Answer 1

Hint: Find the relation between acceleration and velocity. The velocity will be maximum in simple harmonic motion , when the acceleration is zero. Find the position where the acceleration is zero. We can also derive that the acceleration is zero if the net displacement is zero.

Complete answer:
The acceleration is the change in velocity with respect to me. If the velocity of the simple harmonic motion is maximum, the acceleration must be equal to zero. The acceleration is equal to zero only when the particle or object is at initial position or if the displacement of the particle is zero. We know, the displacement of a particle is zero when the particle doesn’t change its initial position or it comes to the initial position after a certain time period. Therefore, the particle will have maximum velocity at the central position and minimum at the extreme positions.

So, the correct answer is “Option B”.

Additional Information:
If we note down the total energies at the initial position and the extreme position, we can observe the kinetic energy of the particle is maximum at the initial position and the potential energy is zero. Also, if we check the energy total at the extreme positions, the kinetic energy will be zero and the potential energy is present as the body gains or goes to a height when oscillating. In a simple harmonic motion, the displacement and velocity differ in the phase by an angle of ninety degrees.

Note:
In any simple harmonic motion, every oscillation will not be simple harmonic, tiny oscillations will not be simple harmonic in most cases. Also, the velocity is a vector so we have to mention the direction of the velocity vector when solving, which is always directed to the initial or centre of the simple harmonic motion.