Question

In simple harmonic motion, when is the magnitude of the acceleration the greatest?

when the potential energy is a maximum

when the displacement is a zero

when the speed is a maximum

when the magnitude of the displacement is a maximum

when the kinetic energy is a minimum

**Please explain why, thanks!

Answer 1

Ans:

The magnitude of the acceleration is the greatest when the magnitude of the displacment is maximum,

as Force is directly proportional to displacement in simple harmonic motion.

This is other way of saying, potential energy stored in the system is maximum( u is directly proportional to displacment squared) and kinetic energy is minimum. (energy conservation U + KE = fixed, if U = maximum, then KE = minimum)

Therefore greatest acceleration = maximum displacment, maximum potential energy and minimum kinetic energy.

Hence option 1) , 4) and 5) are true.