Spring Acceleration: Does Velocity = 0 Mean a = 0?

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When a weight attached to a spring is released, it reaches a point where its velocity is zero at the lowest position. However, the acceleration at this point is not zero; it is directed upwards due to gravitational force. The confusion arises from the relationship between velocity and acceleration, where acceleration is defined as the rate of change of velocity. In simple harmonic motion (S.H.M.), the acceleration is maximum when the displacement is maximum, which occurs at the lowest point of the spring's motion. Therefore, while velocity is zero at this point, the acceleration is at its peak, confirming that velocity being zero does not imply acceleration is also zero.
IKonquer
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Lets say you attach a weight to a spring and release it from rest. When the spring reaches its lowest point, its velocity is zero. What I am confused about is the acceleration of the spring at the bottom. My professor said that the acceleration of the weight at the bottom is g upwards. Intuitively that makes sense to me but not mathematically. dv/dt = a. And if the velocity is 0 at that instant, shouldn't the acceleration also be zero?

Thanks in advance.
 
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a=dv/dt is right. But since the mass executes S.H.M, a=-ω2x.
When the mass reaches its lowest point, x is not 0. Infact, x is max and hence a is max.
Acceleration is instantaneosly 0 only when it crosses its mean position.
 
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