Kuliah Mekanika (Dr. Lutfi R,) Universitas Jember [TA 14/15/Genap] MEKANIKA Dr. Lutfi Rohman 1.

Kuliah Mekanika (Dr. Lutfi R,) Universitas Jember [TA 14/15/Genap]Kuliah Mekanika (Dr. Lutfi R,) Universitas Jember [TA 14/15/Genap]

MEKANIKA

Dr. Lutfi Rohman

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Kuliah Mekanika (Dr. Lutfi R,) Universitas Jember [TA 14/15/Genap]

CHAPTER3Kuliah 3:

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Kuliah Mekanika (Dr. Lutfi R,) Universitas Jember [TA 14/15/Genap]

(Linear Oscillations)

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Kuliah Mekanika (Dr. Lutfi R,) Universitas Jember [TA 14/15/Genap]

Simple Harmonic Oscillator

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The equation of motion for the simple harmonic oscillator

Kuliah Mekanika (Dr. Lutfi R,) Universitas Jember [TA 14/15/Genap]

Energi

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Periode, frekuensi dan kecepatan

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Kuliah Mekanika (Dr. Lutfi R,) Universitas Jember [TA 14/15/Genap]

Harmonic Oscillations in Two Dimensions

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Kuliah Mekanika (Dr. Lutfi R,) Universitas Jember [TA 14/15/Genap]

Phase Diagrams

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The state of motion of a one-dimensional oscillator, such as that discussed in previous Section , will be completely spec-ified as a function of time if two quantities are given at one instant of time, that is, the initial conditions x(t0) and v (t0) (Two quantities are needed because the differential equa-tion for the motion is of second order.). We may consider the quantities x(t) and v(t) to be the coordinates of a point in a two-dimensional space, called phase space.

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Phase diagram for a simple harmonic oscillator for a variety of total energies E.

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Damped Oscillations

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The motion represented by the simple harmonic oscillator is termed a free oscillation; once set into oscillation, the motion would never cease. This oversimplifies the actual physical case, in which dissipative or frictional forces would eventually damp the motion to the point that the oscillations would no longer occur. We can analyze the motion in such a case by incorporating into the differential equation a term representing the damping force. It does not seem reasonable that the damping force should, in general, depend on the displacement, but it could be a function of the velocity or perhaps of some higher time derivative of the displacement. It is frequently assumed that the damping force is a linear function of the velocity,* Fd = v.

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Kuliah Mekanika (Dr. Lutfi R,) Universitas Jember [TA 14/15/Genap]

Underdamped Motion

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Kuliah Mekanika (Dr. Lutfi R,) Universitas Jember [TA 14/15/Genap]

Tugas 3, Kerjakan Soal-soal Berikut:

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