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Essential idea: The solution of the harmonic oscillator can be framed around the variation of kinetic and potential energy in the system.
Nature of science:
Insights: The equation for simple harmonic motion (SHM) can be solved analytically and numerically. Physicists use such solutions to help them to visualize the behaviour of the oscillator. The use of the equations is very powerful as any oscillation can be described in terms of a combination of harmonic oscillators. Numerical modelling of oscillators is important in the design of electrical circuits. (1.11)
For addition information please see this page produced by Tim Brzezinski: Graphing Sine and Cosine Functions
The SHM Equations:
The SHM Equations:
Keys to Success:
Where are you starting from? Stated in the problem.
All Calculations are in rads. Check your MODE.
Be careful with negative displacement (x = -0.3m) values in the instantaneous velocity and kinetic energy equations. Know your order of operations!!!
The total energy in the simple harmonic motion of a particle is:
Directly proportional to its mass
Directly proportional to the square of the frequency of oscillations and
Directly proportional to the square of the amplitude of oscillation.
Position v. Time
Position v. Time
From Equilibrium:
The Blue Wave is a sine wave. Modeled with the equation:
From Max Displacement:
The RED Wave is a cosine wave. Modeled with the equation:
Velocity v. Time
Velocity v. Time
From Equilibrium:
The Blue Wave is a cosine wave. Modeled with the equation:
From Max Equilibrium:
The RED Wave is a NEGATIVE sine wave. Modeled with the equation:
Acceleration v. Time
Acceleration v. Time
This equation is NOT in the IB Physics Data Booklet.
From Equilibrium:
The Blue Wave is a NEGATIVE sine wave. Modeled with the equation:
From Max Displacement:
The Red Wave is a NEGATIVE cosine wave. Modeled with the equation:
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