Simple Harmonic Motion Flashcards
What is simple Harmonic Motion?
An oscillatory motion in which acceleration is directly proportional to displace men and is always directed towards the equilibrium position
A = -constant x displacement (x)
What is the equation for acceleration in Simple Harmonic Motion?
A = -v^2/r = -w^2r
Describe the acceleration of a body in SHM
The body is always accelerating towards the Centre of the Motion except at the center of the Motion where the acceleration is zero.
Think of a pendulum where the acceleration is at its max acceleration at the end but zero. In the middle as that is the equilibrium position.
Describe why a body in SHM keeps swinging past the equilibrium position
A restoring force tries to return the system to equilibrium
The system has inertia and overshoots the equilibrium position
What is the mathematical expression for displacement in SHM?
A = -w^2x where w = 2(pi)f
Therefore
Displacement x = acos (wt)
And x = asin (wt)
What is the equation for hookes law?
F = kx or -kx if force is the restoring force
How is time period calculated in a mass-spring system?
T = 2(pi) root m/k
Gotten by combining hookes law with acceleration in circular motion
Why does an object oscillate with SHM? What is the equation for time period in a pendulum?
Acceleration is proportional to the displacement from equilibrium and always acts towards it.
T = 2(Pi) root L/g
What is the speed equation in SHM
V = +/- w root A^2 - x^2
How is energy calculated in SHM?
Ep = 1/2kx^2
ET = 1/2kA^2
ET = Ek + Ep
Ek = 1/2k(A^2 - x^2)
What is the curve in an energy displacement graph in SHM
Potential energy is a parabolic curve
Kinetic energy is an inverted parabola
The sum of Ek and Ep is always 1/w kA^2
What is damping in oscillation
The dissipation of energy over time
What are the types of damping?
Light, critical and heavy
Describe light, critical and heavy damping
- Light damping: Defined oscillations are observed, but the amplitude of oscillation is reduced gradually with time. The oscillation of a child on a swing without periodic push will loose its energy gradually and be lightly damped.
- Critical Damping: The system returns to its equilibrium position in the shortest possible time without any oscillation. Critical Damping is important so as to prevent a large number of oscillations and there being too long a time when the system cannot respond to further disturbances. Instruments such as balances and electrical meters are critically damped so that the pointer moves quickly to the correct position without oscillating.
- Heavy Damping: The system returns to the equilibrium position very slowly, without any oscillation. Heavy damping occurs when the resistive forces exceed those of critical damping. A push tap in a public toilet is an example of Heavy Damping.
What happens when the applied frequency becomes larger than the resonant frequency of the mass-spring system?
- the amplitude of oscillations decreases more and more,
- the phase difference between the displacement and the periodic force increases from 𝜋/2 until the displacement is 𝜋 radians out of phase with the periodic force.
