Flashcards
PH10053 - Sergey's Theory
Cards in this deck (18)
- 1Define Periodic MotionMotion of an object that regularly repeats - An the object returns to given position after a fixed time interval - A feature of Simple Harmonic Motion
- 2Name the Force that acts to reduce displacement of an object and return the system to equilibrium.Restoring Force
- 3SHM occurs when...The Restoring Force is linearly proportional to the displacement from from equilibrium and opposite to the direction of the displacement.
- 4A general rule for SHM is:Restoring Force=-k(x)
- 5Name two assumptions:1) No Friction
2) Mass of spring is negligibly small in comparison to the mass of the block. - 6When an object is displaced, the spring exerts a ...... ...... equal to ....Restoring Force ; (-kx) where k is the force constant.
- 7What's the differential equation for simple harmonic motion? What's its general solution?(d^2x/dt^2)+(w^2)x=0
x=Acos(wt+d) - 8Quantities: Period (T) Frequency (f) Angular Frequency (w)Equations and Units: Period (s)
Frequency --> f=1/T (Hz)
Angular Frequency --> w=2πf (rad/s) - 9Differentiating the general solution: x=Acos(wt+d) gives: v=... and a=...v=-Awsin(wt+d)
a=-A(w^2)cos(wt+d) = -(w^2)x - 10Phase difference of Velocity and Displacementπ/2
- 11Velocity is maximum when...Displacement is 0 (Eqm position)
- 12Velocity is 0 when...Displacement is maximum (Amplitude of oscillation)
- 13The frequency and period are related to the stiffness (k) of the spring and the particle mass; where w= sqrt(k/m)f=w/2π=(sqrt(k/m))/2π
T=1/f= 2π(sqrt(m/k)) - 14When is the spring constant not constant?When oscillations are large
- 15What's the equation for the vertical displacement in equilibrium when a mass is attached to a spring?y.=mg/k
- 16y' for vertical oscillations is the...Amplitude of oscillations about the equilibrium position of the system when the mass is attached.
Where y'=y-y., where y is the total amplitude from the eqm position without the mass attached - 17Eqm Position: y.=mg/k Hence, mg-ky.=0 Write the equation for vertical oscillations:mg-ky.=ma
by Newton's (II) Law
This translates to:
m((d^2)y/d(t^2))+ky.=mg
(x(1/m)) --> ((d^2)y/d(t^2))+ (k/m)y.=g;
where (k/m) = w - 18—
Information
- Description
- Simple Harmonic Motion- Damped Oscillations - Harmonics
- Created by
- Noah Bryan · Oct 2017
- Updated
- Oct 30, 2017
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