On a nice spring day you find yourself relaxing under an old oak tree. You pull the end of one of the tree's branches down (negative maximum displacement) about 2 ft and let it go (t = 0 s). You note that the resulting motion appears to be from a simple harmonic oscillator with a period of about 2.5 seconds. It takes the branch about 8 oscillations to decrease the amplitude by a factor of 2. (a) What evidence could you have to claim the branch undergoes simple harmonic motion? (be brief) (b) Describe the energy transfers in the branch + earth system during an entire cycle of the motion. Focus on the three most important types of energy in the system. Feel free to use a plot or diagram to illustrate how/ when the energy changes forms. (c) What is the time constant τ for the amplitude as a function of time during the damping of the oscillation.
On a nice spring day you find yourself relaxing under
an old oak tree. You pull the end of one of the tree's branches
down (negative maximum displacement) about 2 ft and let it go
(t = 0 s). You note that the resulting motion appears to be from
a simple harmonic oscillator with a period of about 2.5 seconds.
It takes the branch about 8 oscillations to decrease the amplitude
by a factor of 2.
(a) What evidence could you have to claim the branch undergoes
(b) Describe the energy transfers in the branch + earth system during an entire cycle of the motion. Focus on
the three most important types of energy in the system. Feel free to use a plot or diagram to illustrate how/
when the energy changes forms.
(c) What is the time constant τ for the amplitude as a function of time during the damping of the oscillation.
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