Ch 1 Oscillatory Motion

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Ch 1 Oscillatory Motion

• Examples

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• Example 1 An object oscillates with simple
  harmonic motion along the x axis. Its position
  varies with time according to the equation
• where t is in seconds and the angles in radians.
• (A) Determine the amplitude, frequency, and
  period of the motion.
• Solution Compare the last equation by the
  equation

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B) Calculate the velocity and acceleration of the
object at any time t.
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c) Using the results of part (B), determine the
position, velocity, and acceleration of the
object at t 1.00 s.
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(D) Determine the maximum speed and maximum
acceleration of the object.
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Example 2 A 200-g block connected to a light
spring for which the force constant is 5.00 N/m
is free to oscillate on a horizontal,
frictionless surface. The block is displaced 5.00
cm from equilibrium and released from rest. (A)
Find the period of its motion.
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(B) Determine the maximum speed of the block.
(C) What is the maximum acceleration of the
block?
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(D) Express the position, speed, and acceleration
as functions of time.
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• What if the block is released from the same
  initial position, xi 5.00 cm, but with an
  initial velocity of vi - 0.100 m/s? Which parts
  of the solution change and what are the new
  answers for those that do change?
• Answers Part (A) does not changethe period is
  independent of how the oscillator is set into
  motion.
• Parts (B), (C), and (D) will change. We begin by
  considering position and
• velocity expressions for the initial conditions

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Parts (B), (C), and (D) will change. We begin by
considering position and velocity expressions for
the initial conditions
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