# Mechanical energy of a spring system

## Homework Statement

A damped mass-spring 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?
Part 2: How much energy is dissipated in the ﬁrst
period (8.7 s interval)?

Part 3: How much energy is dissipated in the second
period (8.7 s interval)?

## 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

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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