Simple harmonic motion Flashcards
What is the necessary condition for simple harmonic motion (SHM)?
Acceleration of a particle proportional too displacement in the opposite direction
a=-kx
In the equation denoting simple harmonic motion as a=-kx, what is the constant k?
ω² ~ angular velocity²
Where in the cycle is the particle’s velocity a maximum?
The centre of its oscillation (Velocity = 0 at maximum displacement)
Where in the cycle is the particle’s Acceleration a maximum?
When the displacement of the particle is at a maximum (acceleration = 0 at centre of oscillation)
What is the relationship between acceleration and displacement?
Acceleration is the rate of change of the rate of change (velocity) of displacement
How do you calculate the maximum velocity?
Vmax = ω.A
What trig function generally maps the graph of displacement /time ?
Cosine
What equation (hint: graphical) links displacement, amplitude, angular velocity and time?
x = A cos(ωt)
How do you interpret amplitude and time period from a displacement time graph?
Amplitude = Maximum displacement (if cosine, y intercept)
Time period = period of curve
What equation (hint: graphical) links velocity, amplitude, angular velocity and time?
V = -ω.A.Sin(ωt)
What equation (hint: graphical) links acceleration, amplitude, angular velocity and time?
a = -ω².A.Cos(ωt)
What is the relationship between acceleration, velocity and displacement?
da/dt = v
dv/dt = x
What trig function generally maps the graph of velocity /time ?
-Sine (NEGATIVE)
What trig function generally maps the graph of acceleration /time ?
-Cosine (NEGATIVE)
How is the total energy against time represented on a graph in an ideal simple harmonic system?
A straight line through the y axis
Ep+Ek = constant
