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 zero $\left(x=0\right)$

• The velocity of an oscillator in SHM is defined by:

$v=v_0\cos \omega t$

• Where:

  • $v$ = velocity (m s^-1)

  • $v_0$ = maximum velocity (m s^-1)

  • $\omega$ = 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 $t=0$)

• The velocity $v$ of an oscillator is related to its displacement $x$ by:

$v=\pm \omega \sqrt{x_0^2-x^2}$

• Where:

  • $x$ = displacement (m)

  • $x_0$ = amplitude (m)

  • ± = ‘plus or minus’. The value can be negative or positive

• This equation shows that

  • The greater the amplitude $x_0$ of an oscillation, the greater its velocity $v$ when passing through the equilibrium position (at $x=0$)

• The maximum velocity $v_0$ of an oscillator is therefore given by:

$v_0=\omega x_0$

The variation of the speed of a mass on a spring in SHM over one complete cycle