- #1
RoyceB
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Homework Statement
The amplitude of vibration of a mass on a horizontal spring experiencing SHM is = 0.13m. The mass is 85g and the force constant is 55N/m. a) What is the maximum elastic potential energy of the system. b) Find the speed of the mass when it's position is x = 7.4cm from the equilibrium point. c) What is it's maximum speed?
A = 0.13m
m = 0.085Kg
k = 55N/m
Δx = 0.074m
Homework Equations
Ee = ½k(Δx)2
Ek = ½mv2
Fx = -kΔx
T = 2π√(m/k)
Fc = mv2 / A[/B]
The Attempt at a Solution
a)
For this I simply used the Ee equation and solved for it. I used 0.13m as the amplitude as I figured this is the furthest the spring could stretch out.
Ee = ½k(Δx)2[/B]
Ee = ½55N/m(0.13)2
Ee = 0.46J
b)
This one I solved for T, used the force equation and the Fc equation to solve for speed.
T = 2π√(m/k)
T = 2π√(0.086/55)
T = 0.25s
Fx = -kΔx
Fx = -55(0.074)
Fx = 4.07N
Fc = mv2 / A
Fc = (0.086)v2 / 0.13
v = 2.5m/s
c) I am kind of lost and thought of making Ee = Ek but would like some assistance.
Also if you could proof check my answers and tell me any errors as I assume my entire b) part maybe wrong.