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36 Cards in this Set
- Front
- Back
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What is the equation for angular frequency? |
Omega = 2*Pi*frequency |
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What is the formula for frequency? |
frequency = 1/time |
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What is the equation for the restoring force? |
F=-kx |
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What is the restoring force equation assuming? |
That there is no friction. |
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What is simple harmonic motion? |
When the restoring force is directly proportional to the displacement from equilibrium. It is the projection of uniform circular motion onto a diameter. |
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What is the equation for acceleration in simple harmonic motion? |
a = (-k/m)*m. This acceleration is not constant.
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What is a body that undergoes simple harmonic motion called? |
A harmonic oscillator. |
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When is the restoring force approximately proportional to the displacement? |
If the displacement is sufficiently small. |
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What is the frequency? |
It describes many cycles of oscillation occur per second. |
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What is angular frequency? |
It describes how many radians per second this corresponds to on the reference circle. |
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What do period and frequency not depend on in simple harmonic motion? |
The amplitude. |
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What is true if a body does depend on amplitude? |
Then it is not simple harmonic motion. |
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What is the equation for displacement in simple harmonic motion? |
x=Acos(wt+phi) |
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What type of function is the position in simple harmonic motion? |
Periodic and sinusoidal. |
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What is phi? |
It is the phase angle and tells us at what point in the circle the point Q was at t=0. |
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What is the equation for phi? |
phi=arctan(-v/wx) |
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What is the equation for amplitude in simple harmonic motion? |
a= (x^2+(v^2/w^2))^(1/2) |
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Why is the total mechanical energy in a spring conserved? |
The vertical forces do no work. |
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What is the equation for the total mechanical energy in an ideal spring? |
E=K+U=0.5kA^2 |
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What would happen if x was greater than A? |
U would be greater than E and K would be negative. As K can never be negative , x can never be greater than A. |
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What is kappa? |
Kappa is the torsion constant. |
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What provides the restoring force in a pendulum? |
Gravity. |
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What is the equation for angular frequency for a simple pendulum with a small amplitude? |
Omega = (g/L)^(1/2) |
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What is the equation for frequency for a simple pendulum with a small amplitude? |
f= 1/(2*pi)*(L/g)^(1/2) |
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What is the equation for time for a simple pendulum with a small amplitude? |
T=2*pi*(L/g)^(1/2) |
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What would happen to the restoring force if g was increased? |
The frequency would increase and the period would decrease. |
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What is the equation for angular frequency for a physical pendulum? |
omega={(m*g*d)/I}^(1/2) |
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What is the equation for time for a physical pendulum? |
T=2*pi*{T/(m*g*d)}^(1/2) |
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What is damping? |
The decrease in amplitude due to dissipative forces and the corresponding motion is called damped oscillation. |
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What is the equation for the distance for an oscillator with little damping? |
x=Ae^(-(b/2m)t)*cos(wt+phi) |
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What is the equation for angular frequency for an oscillator with little damping? |
w={(k/m)-(b^2/4m^2)}^(1/2) |
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What condition occurs when k/m - b^2/4m^2 = 0? |
Critical damping. |
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What condition occurs if b is greater than 2*(km)^(1/2)? |
Overdamping. |
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Why is the damping force non-conservative in damped oscillations? |
The mechanical energy of the system is not constant but decreases continuously, approaching zero for a long time. |
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What is the equation for the rate of change of energy? |
dE/dt = -bv^2 |
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What motion is the result of applying a periodically varying driving force with angular frequency, w, to a damped harmonic oscillator? |
Forced oscillation. |
