
Concept explainers
If the acceleration of a simple harmonic oscillator is ever zero.

Answer to Problem 1Q
Solution:
The acceleration is zero at the place where displacement is equal to zero and when the velocity is at its maximum, at the equilibrium position.
Explanation of Solution
The acceleration is zero at the place where displacement is equal to zero.
At the point in the centre, the acceleration drops to zero and changes direction when the velocity changes from increasing to decreasing.
The acceleration is zero as it crosses the equilibrium point.
The acceleration is zero when the velocity is at its maximum, that is, at the equilibrium position. Since the force and hence the acceleration always acts towards the equilibrium position (because it is a restorative force), then the force and acceleration must change their sign as the mass crosses the equilibrium point, and therefore must be zero instantaneously at the equilibrium point. Acceleration changes during
The acceleration also oscillates in simple harmonic motion. If you consider a mass on a spring, when the displacement is zero the acceleration is also zero, because the spring applies no force. When the displacement is maximum, the acceleration is maximum, because the spring applies maximum force; the force applied by the spring is in the opposite direction as the displacement. The acceleration is given by
So, the maximum acceleration is
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