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Oscillations Readings: Chapter 14.

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Presentation on theme: "Oscillations Readings: Chapter 14."— Presentation transcript:

1 Oscillations Readings: Chapter 14

2 Oscillation: Periodic Motion
T – period of motion - frequency

3 Oscillation: Periodic Motion: Simple Harmonic Motion
Simple Harmonic Motion – sinusoidal oscillation or The most general expression for sinusoidal motion - phase constant - amplitude If then

4 Oscillation: Periodic Motion: Simple Harmonic Motion
Example: Uniform circular motion x- component: - angular frequency

5

6 Oscillation: Periodic Motion: Simple Harmonic Motion
T – period of motion (units – s) - amplitude - frequency (units – hertz – Hz =1/s) - phase constant - angular frequency (units – rad/s)

7 - phase constant Phase constant specifies the initial position of the oscillator

8 Simple Harmonic Motion: Position, Velocity, and Acceleration

9 Simple Harmonic Motion: object oscillating on a spring
Newton’s second law: Hooke’s law:

10 Simple Harmonic Motion: Conservation of energy
Kinetic energy: Potential energy: Total energy:

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12 Example: Find the relation between kinetic and potential energy at x=A/3.
The total energy is the sum of kinetic and potential energy. At x=A the kinetic energy is 0. At x=A/3 the potential energy is Then the kinetic energy at this point is Then

13 Simple Harmonic Motion:
If force is proportional to displacement (it is not necessary the spring system) then Solution of this equation:

14 Oscillations about equilibrium position
Net force: Oscillations about equilibrium position

15 The pendulum: small-angle approximation
The net force is the sum of two forces: tension and gravitational force. Tangential component of the net force is If y is the arc length then If y<<l then then

16 If the system has a friction then there is an energy loss
The energy is determined by the amplitude of oscillations, so the energy loss means that the amplitude is decreasing


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