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Homework Statement
A damped massspring system oscillates at
285 Hz. The time constant of the system is
8.8 s. At t = 0 the amplitude of oscillation
is 1.3 cm and the energy of the oscillating
system is 36 J.
Part 1: What is the amplitude of oscillation at t =
8.7 s?
Answer in units of cm
Part 2: How much energy is dissipated in the ﬁrst
period (8.7 s interval)?
Answer in units of J
Part 3: How much energy is dissipated in the second
period (8.7 s interval)?
Answer in units of J
Homework Equations
A = A(initial) * e^{(t/time constant)}
E = E(initial) * e^{(t/time constant)}
I followed the method of the attached picture and couldn't get the correct answer.
The Attempt at a Solution
Part 1: Answered correctly:
A(8.7 s) = (1.3 cm) * e^{(8.7/8.8)} = 0.4837088518 cm
Part 2:
Change in mechanical energy between 0 and 7.8 seconds:
ΔE = E(initial) * (e^{(8.7/8.8)}  e^{(0/8.8)})
ΔE = (36 J) * (e^{(8.7/8.8)}  1)
ΔE = 22.604985 J
Which was incorrect
Part 3:
ΔE = (36 J) * (e^{(17.4/8.8)}  e^{(8.7/8.8)})
ΔE = 8.4109474 J
Which was also incorrect.
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