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## Homework Statement

A mass of .4 kg is connected to a spring with a spring constant of 100 N/m, slides on a frictionless horizontal surface in simple harmonic motion, Its maximum displacement is .3m?

What is the maximum speed of the mass?

What is the energy stored in gthe mass/spring system when its speed is half the maximum value?

What is acceleration of t he mass when its speed is half the maximum value?

## Homework Equations

m=.4kg

k=100N/m

A(max displacement)=.3m

## The Attempt at a Solution

What is the maximum speed of the mass?

Vmax=ωA=√k/m(A)=√100/.4 (.3)=4.74m/s CORRECT????

What is the energy stored in gthe mass/spring system when its speed is half the maximum value?

PE=KE

1/2k(A)2 = 1/2m(v)2 so....

1/2(100)(.3)2 = 1/2(.4)(4.74)

4.50 = 4.50

so....1/2(.4)(4.74/2)2 = 1.12J IS THIS CORRECT????

What is acceleration of t he mass when its speed is half the maximum value?

amax=A(ω)2, but where would I use the speed half max value?

I would really like to learn this. It's been 20+ years since I have taken a Physics course.

Thank you!