Question

A box of mass m on an ideal spring vibrates in a vertical plane between points A and E as shown in above figure. At which point is the acceleration of the box the greatest?

• A. A
• B. B
• C. C
• D. D
• E. The acceleration is the same at all points

Answer 1

The correct option is A A

From the Hooke's law, the force acting at the end of a spring=$F=-kx$

where $x$ is the displacement of the end from the equilibrium position $C$.

Hence the acceleration due to spring=$\frac{F}{m}$ is maximum at $A$ and $E$ with opposite direction.

However gravitation would increase the acceleration at point A being in the same direction, and would reduce that at E.

Hence acceleration of box is greatest at A.