A mass is suspended vertically from a spring so it is at rest at the equilibrium position. The mass is pulled a short distance straight down and released so that it oscillates about the equilibrium position. The acceleration of the mass is zero when the mass is
Question
A mass is suspended vertically from a spring so it is at rest at the equilibrium position. The mass is pulled a short distance straight down and released so that it oscillates about the equilibrium position. The acceleration of the mass is zero when the mass is
Solution
The acceleration of the mass is zero when the mass is at the equilibrium position. This is because at the equilibrium position, the force due to the spring (which follows Hooke's law, F = -kx, where k is the spring constant and x is the displacement from equilibrium) is zero, and therefore the acceleration (which follows Newton's second law, F = ma, where m is the mass and a is the acceleration) is also zero.
Additionally, the acceleration is also zero at the maximum displacement from the equilibrium position (either at the top or bottom of the oscillation). This is because at these points, the velocity of the mass is zero (it momentarily stops before changing direction), and acceleration is the rate of change of velocity. However, it's important to note that while the acceleration is zero at these points, the force is not - the spring is either fully compressed or fully extended, so the force (and therefore the potential energy) is at a maximum.
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