How Do You Calculate Dynamics of a Mass Spring System?

[deliliah]

Homework Statement

a mass spring system vibrates with an amplitude of 4.5 cm. if the spring has a constant od 250 n/m and the mass is 400 kg determine the
a) total mechanical energy
b) the maximum speed of the mass
c) the maximum acceleration
d) the speed of the mass when the displacement is 2.0 cm

Homework Equations

e= 1/2mv^2 + 1/2 kx^2
e= 1/2 ka^2 = 1/2 mv^2(max)
e=1/2 mv^2 + 1/2 kx^2
e= 1/2 mv^2 + mgh

The Attempt at a Solution

1/2 (400)(0)^2 + 1/2 (250)(4.5)^2= 2531.25?

 

[Dick]

If the amplitude is 4.5 cm then when x=4.5 cm, then v=0. Can you start with that?

 

[deliliah]

so would i just use the 1/2 mv^2 + 1/2 kx^2 for the total mechanical energy? and just plug in 4.5 for x and 0 for v?

 

[collinsmark]

1/2 (400)(0)^2 + 1/2 (250)(4.5)^2= 2531.25?

so would i just use the 1/2 mv^2 + 1/2 kx^2 for the total mechanical energy? and just plug in 4.5 for x and 0 for v?

Yes, that will work. But make sure you convert 4.5 cm to meters, if you want your final answer in units of Joules.