Describe the energy transfers taking place when a spring SHM system is moving. Describe the energy present at each of the three extreme points (ie. minimum, equilibrium, and maximum).

Question

Describe the energy transfers taking place when a spring SHM system is moving. Describe the energy present at each of the three extreme points (ie. minimum, equilibrium, and maximum).

Answer 1

Total energy in SHM is conserved

E = K+U=constant

E = (1/2)mv² + (1/2)kx²

Equilibrium is when the system is not displaced (x=0)

E =(1/2)mv² + (1/2)kx²

E = (1/2)mv² all of the energy is covered into kinetic energy and the velocity is a maximum

Minimum is when the system is maximally compressed (x = -A) and it is stopped (v=0) as it changes direction

E = (1/2)mv² + (1/2)k(-A)²

E = (1/2)kA² all of the energy is stored as spring potential energy

Maximum is when the system is maximally stretched (x = A) and it is stopped (v=0) as it changes direction

E = (1/2)mv² + (1/2)k(A)²

E=(1/2)kA² all of the energy is stored as spring potential energy (just like the minimum point)