- #1

- 110

- 0

An oscillating mass is hung from a vertical spring. Take the potential energy of the system when the spring is at the unstretched length to be zero for both spring and gravity. Calculate the gravitational potential energy, spring potential energy, and total potential energy of the system at:

Equilibrium

y cm above equilibrium

y cm below equilibrium

(Assume the spring can compress more than y and that F = -kΔx still holds)

Relative equations:

GPE = mgh

SPE = ½ k x^2

Work so far:

Equilibrium GPE = mgh

Equilibrium SPE = ½kh^2

Equilibrium TE = mgh + ½kh^2

y cm above GPE = mg(h-y)

y cm above SPE = ½k(h-y)

y cm above TE = mg(h-y) + ½k(h-y)

y cm below GPE = mg(h+y)

y cm below SPE = ½k(h+y)

y cm below TE = mg(h+y) + ½k(h+y)