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Transcript 
Pendulum:
Problem: Consider the simple pendulum (mass at the end of a
rod or string) as shown below.
If we start from the rotational (torque) version of Newton’s 2nd
Law of Motion,
Section 3.4
Copyright©Arunabha Biswas
177
Section 3.4
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178
Find the general solution of the linearized DE.
Use your solution to predict the period of the oscillation of a
pendulum.
Section 3.4
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Comment: What does it mean about the swinging of a
pendulum for larger angles?
Section 3.4
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180
Mass-spring system with external force:
Problem: Write down the DE for for this system when
Fext = A sin (Bt)
Section 3.4
Copyright©Arunabha Biswas
181
Problem: Sketch an RLC circuit, with voltage supply
−A
(electromotive force or EMF) of E(t) =
cos (Bt), and write
B
down the DE for the current in the circuit.
Example: Radio waves, AC
Section 3.4
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182
Comment on the similarity between the mathematical model of
the mass-spring system and of the RLC circuit.
Section 3.4
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183
Unforced motion:
Setting Fext = 0, review the effect of increasing the friction
coefficient c on the solution yc .
What is yp solution in a mass-spring system? And why it is
called so?
Section 3.4
Copyright©Arunabha Biswas
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