Calculate the total energy of the mass spring system

[AClass]

Homework Statement

A 12Kg mass udnergoes simple harmonic motion with an amplitude of 10cm. If the force constant for the spring is 320 N/m

a) Calculate the total energy of the mass spring system.
b) Calculate the maximum speed of the mass
c) Calculate the speed of the mass when it is 5.0cm from the equilibrium point.

Homework Equations

Fx= -kx
a=kx/m
ET=(0.5)mv^2 +(0.5)kx^2
Et=(0.5)(m)(A)^2

The Attempt at a Solution

a)

ET=(0.5)(320 N/m)(0.10m)^2
ET= 1.6J

b)

1.6J=(0.5)(12kg)(V)^2 + (0.5)(320N/m)(0)
v=0.52m/s

c)

1.6J=(0.5)(12kg)(V)^2 +(0.5)(320N/m)(0.05m)^2
v=0.45m/s

Could someone verify this for me? Thanks

 

[rock.freak667]

Those look correct to me (the method, I did not check the numbers).

 

[Alphonce R]

1.a) E=1/2KA^2=1/2(320N/m)(0.1m)^2=1.6J b) V(max)=wA