Module 5 Simple Harmonic Motion Flashcards
Where is velocity at a maximum?
at the mean position when x = 0
Where is velocity zero?
at the amplitude when x = +A or -A
Explain why at the amplitude, velocity is zero?
mass is changing direction, velocity zero for an instant
What is the definition for amplitude considering SHM?
the maximum displacement from the equilibrium/mean position
Explain how a graph of displacement against time and acceleration against time can be used to show that they are directly proportional but in opposite directions?
Comparison of the two graphs shows a phase difference of 180°
Define simple harmonic oscillation?
a type of oscillation where acceleration is directly proportional to displacement but in the opposite direction
What is the symbol for angular displacement?
omega ω
What are the units for ω?
the units for angular frequency ω are rad*s^-1
When is the formula x=Asin(ωt) used over x=Acos(ωt) used?
When at t=0 the displacement is zero, use sin
Explain how when using x=Acos(ωt), if t=T where T is the time period, will the displacement be the amplitude
Calculation in radians
ωt=ωT and ω=2π/T
So ωT=2π
cos(2π) = 1
1xA = A
How you find the maximum velocity of an object in SMH?
Vmax=±ωA (originally (A^2-x^2) cancels out to A^2 as displacement x is zero at max velocity)
Describe how to plot a graph of acceleration against displacement
Straight line through the origin
Negative gradient
Need to show A, -A, amax and -amax on the axes
What is the word for a system undergoing SMH with no resistive forces at play?
undamped
For an undamped system, describe the changes in KE and PE as the mass moves from the centre to the amplitude
At x = 0, V = max therefore KE = max, PE = min
At x = A, V = 0 therefore KE = 0, PE = max Loss of KE = Gain in PE
Explain how the height of a pendulum moved can be calculated using energy equations
KE=1/2m(vmax^2) at x = 0
PE=mgh at x = A
Loss from max KE = gain in PE
1/2m(v_max)^2=mgh (mass cancels out)
