SHM Flashcards
What is SHM?
It is when the acceleration of a body is proportional to its displacement but acts in the opposite direction
a ∝ −x
What is the equation of the acceleration of an object in SHM?
a = −⍵^2 x
What does this equation a = −⍵^2 x demonstrate?
- The acceleration reaches its maximum value when the is displacement at maximum(amplitude)
- The negative sign shows that when the object is displacement to the right the acceleration will be acting to the left
Explain how a graph of acceleration against displacement show that an object oscillating with SHM? (2 marks)
- The graph is a straight line though the origin, therefore acceleration is proportional to displacement
- The negative gradient shows that the acceleration acts towards the equilibrium and opposite to the direction of displacement
What are the 2 displacement equations in SHM and when are they used?
- x = Asin(⍵t)
This equation can only be used when an object begins oscillating from the equilibrium position ( x=0 at t= 0 )
Note : the displacement X will be at its maximum when sin(⍵t) equal 1 or -1
- x = Acos(⍵t)
This equation can only be used when an object is oscillating from the amplitude position (x = A or x = -A )
When using the 2 displacement equations, what do you need to make sure is set before using your calculator?
That the calculator is set to radians
How to draw the two graphs of X against t for cos (wt) and sin(wt)?
- Cos graph will start from amplitude ( max displacement)
- Sin graph will start from equilibrium position ( zero)
What wquation to use when trying to find the maximum velocity of an oscillator from the equilibrium position?
v = v0 cos(⍵t)
it is cos because the derivative of sin is cos and velocity is the derivative of displacement
What equation do you use for how the velocity changes with the oscillate displacement?
v = ±ω * √(A² − x²)
What does the equation of how velocity changes with the oscillate displacement shows? And what is the relationship between time and amplitude?
- when the oscillator has greater amplitude, it will have to travel a greater distance in the same time so that’s why it needs to be faster therefore velocity and amplitude are directly proportional.
- When the velocity is at maximum the displacement will be zero and the equation will change from
v = ±ω * √(A² − x²) to v0 = ⍵A
The new equation also shows that velocity and amplitude are directly proportional.
From point one we can see that time and amplitude are independent of each other.
What are the two forms of energy that are always being exchanged in SHM?
KE and PE
PE can be gravitational PE (for a pendulum)or elastic PE ( for a spring)
Or both PEs (for a vertical mass on a spring)
When is KE max at?
KE is max when X= 0 and v= max
When is KE zero at?
KE is zero when x = A or X= -A
When is PE max at?
When x= A or X= -A
Why are flashcards 13 and 14 true?
Because ke is transferred to PE as the height above equili increases, since PE = mgh
SHM system always keeps converting energy. What does this mean for the total energy?
The total energy of a SHM system is always constant.
What does the total energy of SHM equal to?
KE + PE
