# Mechanical energy of a spring system

**1. The problem statement, all variables and given/known data**

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?

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

**2. Relevant 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.

**3. 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.

http://ift.tt/1ewH9ai

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