Question

If a mass on a spring is in simple harmonic motion, which of the following is true when the speed of the system is largest?

     (A)  Magnitude of acceleration is at maximum  and  Potential Energy is at maximum

     (B)  Magnitude of acceleration is at minimum  and  Potential Energy is at maximum

     (C)  Magnitude of acceleration is zero   and  Potential Energy is zero

     (D)  Magnitude of acceleration is zero   and  Potential Energy is at maximum

     (E)  Magnitude of acceleration is at maximum  and Potential Energy is zero

Answer 1

Total energy of the system in simple harmonic motion is the sum of the kinetic energy of the block and the potential energy of the spring.

When the speed of the mass is maximum the kinetic energy of the block is maximum and it is maximum when the total energy is equal to the kinetic energy of the block.

Therefore the potential energy of the spring at this point is zero.

The potential energy of the spring is zero therefore the extension of the spring is zero.

When the extension of the spring is zero it exerts a zero force on the mass meaning the acceleration of the mass is zero.

When the speed of the system is largest :

Magnitude of acceleration is zero and Potential Energy is zero.