Vibrations Flashcards
Define ‘Simple harmonic motion’
When an object moves such that its acceleration is always directed towards a fixed point and is proportional to the distance from the fixed point.
State the equation linked with SHM
a=-ω²x
a=acceleration
ω=angular velocity
x=displacment
Draw a graph for an object travelling with shm
negative gradient, straight line going through origin
a on the y axis and x on the x axis
-ω²=the gradient
As an SHM object moves it’s ____ increases a it goes further from it’s______ _____.
Acceleration increases
equilibrium position
If a=0m/s² when x=0m what a be if x is at its maximum (x=A)
a will also be at its maximum
so a max=-ω²A
A=maximum amplitude
Give the equation for the displacement of an oscillating object at a certain time
x=Acos(ωt+ ε)
ε =phase constant
for the displacement of an oscillating object at a certain time, ε is equal to what if t=0 and x=max
ε=0
for the displacement of an oscillating object at a certain time, ε is equal to what if t=0 and x=0
ε=π/2
How to calculate velocity using x=Acos(ωt+ ε)
V=-Aωsin(ωt+ε)
How to calculate maximum velocity using x=Acos(ωt+ ε)
sin(ωt+ε) max value is 1
so Vmax=-Aω x 1
Vmax=-Aω
What do both SHM equations show
The equations show that both x and v vary sinusoidally with time during SHM.
vmax when x=0m and vice versa
Describe a velocity time graph for SHM
Sine wave
V begins negative (due to x being positive)
Describe a displacement time graph for SHM
Sine wave
Displacement always begins at maximum
Describe the energy of body during SHM
A body during SHM will have a constant energy but it will transfer from potential to kinetic energy.
When Ek is max, Ep=0J and vise versa
State two examples of SHM
Two common examples of SHM are masses on a spring and a
simple pendulum.
