Please Help with Physics Problem?

Question

A mass sitting on a horizontal, frictionless surface is attached to one end of a spring; the other end is fixed to a wall. 6.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, it experiences a maximum acceleration of 20 m/s2.

1. Find the value of the spring constant.

2. Find the value of the mass.

All work would be greatly appreciated. Thank you =).

Answer 1

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The compression of the spring = x = 0.12 m.

Work done in compressing the spring = w =6.0 J

Force constant of spring = k

Work done in compressing the spring = W =(1/2)kx^2

k= 2W/x^2

k =2*6/( 0.12 )^2

k = 10000 /12 = 833.333 N/m

1 .The value of the spring constant is 833.333N/m

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Mass = m

Amplitude =A=0.12 m

Angular frequency =w = sq rt k /m

Maximum acceleration = a = Aw^2=Ak/m

Maximum acceleration = a = 20 m/s^2

Ak/m =20

m= Ak /20

m =0.12*833.333 / 20= 5 kg

2. The value of the mass is 5 kg

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Answer 2

The total energy of the system is 6.0 J. The Amplitude is .12 m. Therefore

E = 1/2 k A²

Solve for the spring constant k.

Then F = ma = kA

Solve for the mass m.

Answer 3

Here's a partial.
The acceleration is 2G, But it is 0 after the spring sproings. Figure 1G over that 0.12 meters.
Put the mass vertically, and spring it, I'd say it would continue 0.12 meter higher than the spring.
How much does a mass have if it takes 6J to raise it 0.12 meters?
Spring constant? Beats me.