# Energy in an Oscillating Spring

## Homework Statement

A mass of 240 g oscillates on a horizontal frictionless surface at a frequency of 3.0 Hz and with amplitude of 4.5 cm.
a) What is the effective spring constant for this motion?
b) How much energy is involved in this motion

m = 240 g = 0.24 kg
A = 4.5 cm = 0.045 m
f = 3.0 Hz
g = 9.8 m/s^2

## Homework Equations

k= F/x = mg/x
E = K + U
K = 1/2*m*v^2
U = 1/2*k*x^2
v = ±ε√(A^2-x^2)
ε = 2πf = √(k/m)
v=0 when x=±A since the object stops briefly before travelling back towards the equilibrium.
^^^ That means K=0

## The Attempt at a Solution

a) k= F/x = mg/x = [(0.240 kg)(9.8 m/s^2)]/(0.045 m) ≈ 52.27 N/m

b) E = 1/2*(52.27 N/m)(.045m)^2 = 0.053 J

^^^ Does this all look correct?

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Delphi51
Homework Helper
a) k= F/x = mg/x
Why this formula? We aren't given the force of the spring and it will not be related to gravity in this situation - "on a horizontal surface". Use a different spring formula that makes use of one of the given quantities.

b) should be okay once you have the correct value for k.

SammyS
Staff Emeritus
Homework Helper
Gold Member

## Homework Statement

A mass of 240 g oscillates on a horizontal frictionless surface at a frequency of 3.0 Hz and with amplitude of 4.5 cm.
a) What is the effective spring constant for this motion?
b) How much energy is involved in this motion

m = 240 g = 0.24 kg
A = 4.5 cm = 0.045 m
f = 3.0 Hz
g = 9.8 m/s^2

## Homework Equations

k= F/x = mg/x
E = K + U
K = 1/2*m*v^2
U = 1/2*k*x^2
v = ±ε√(A^2-x^2)
ε = 2πf = √(k/m)
v=0 when x=±A since the object stops briefly before travelling back towards the equilibrium.
^^^ That means K=0

## The Attempt at a Solution

a) k= F/x = mg/x = [(0.240 kg)(9.8 m/s^2)]/(0.045 m) ≈ 52.27 N/m

b) E = 1/2*(52.27 N/m)(.045m)^2 = 0.053 J

^^^ Does this all look correct?
Solve : 2πf = √(k/m) for k.

Thanks for the tips!

Ok, so solving for k in 2πf = √(k/m) gets me k = 4m(πf)^2.
So, k = 4*(.240 kg)*(3.0 Hz)^2*(π)^2 ≈ 85.27 N/m

For part b, using the new k value gets me an answer of approximately 0.086 J. Is that correct?