Velocity (OCR A Level Physics)
Revision Note
Velocity of an Oscillator
The velocity of an object in simple harmonic motion varies as it oscillates back and forth
Since velocity is a vector, the velocity of the oscillator is its speed in a certain direction
The maximum velocity of an oscillator is at the equilibrium position i.e. when its displacement is 0 (x = 0)
The velocity of an oscillator in SHM is defined by:
v = v0 cos(⍵t)
Where:
v = velocity (m s-1)
v0 = maximum velocity (m s-1)
⍵ = angular frequency (rad s-1)
t = time (s)
This is a cosine function if the object starts oscillating from the equilibrium position (x = 0 when t = 0)
How the velocity v changes with the oscillator’s displacement x is defined by:
Where:
x = displacement (m)
x0 = amplitude (m)
± = ‘plus or minus’. The value can be negative or positive
This equation shows that when an oscillator has a greater amplitude x0, it has to travel a greater distance in the same time and hence has greater velocity, v
When the velocity is at its maximum (at x = 0), the equation becomes:
v0 = ⍵x0
The variation of the speed of a mass on a spring in SHM over one complete cycle
Worked Example
A simple pendulum oscillates with simple harmonic motion with an amplitude of 15 cm. The frequency of the oscillations is 6.7 Hz.
Calculate the speed of the pendulum at a position of 12 cm from the equilibrium position.
Answer:
Step 1: Write out the known quantities
Amplitude of oscillations, x0 = 15 cm = 0.15 m
Displacement at which the speed is to be found, x = 12 cm = 0.12 m
Frequency, f = 6.7 Hz
Step 2: Oscillator speed with displacement equation
Since the speed is being calculated, the ± sign can be removed as direction does not matter in this case
Step 3: Write an expression for the angular frequency
Equation relating angular frequency and normal frequency:
⍵ = 2πf = 2π× 6.7 = 42.097…
Step 4: Substitute in values and calculate
v = 3.789 = 3.8 m s-1 (2 s.f)
Examiner Tips and Tricks
You often have to convert between time period T, frequency f and angular frequency ⍵ for many exam questions – so make sure you revise the equations relating to these:
You've read 0 of your 5 free revision notes this week
Sign up now. It’s free!
Did this page help you?