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 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.

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Question

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.

Definition Definition Special type of oscillation where the force of restoration is directly proportional to the displacement of the object from its mean or initial position. If an object is in motion such that the acceleration of the object is directly proportional to its displacement (which helps the moving object return to its resting position) then the object is said to undergo a simple harmonic motion. An object undergoing SHM always moves like a wave.

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