mass-spring system

• equipment

  • spring
  • 50g masses with 50g holder
  • stand and clamp
  • pin and blu-tack
  • meter ruler
  • stopwatch
• method

  • set up apparatus without masses on holder
  • pull mass hanger vertically downwards a few cm and release
  • start stopwatch when it passes fiducial marker
  • stop stopwatch after 10 complete oscillations and record time
  • divide by 10 to find time period of the system
  • add 50g mass and repeat adding 50g until 500g
  • record total mass and time period for each
  • repeat experiment twice and find the mean time for each mass
• graphs and calculations

  • plot graph of $T^2$ against mass and draw a line of best fit
  • gradient = $\frac{4\pi^2}{k}$
  • $T=$$2\pi\sqrt{\frac{m}{k}}\ \ \rightarrow\ \ T^2=$$\frac{4\pi^2}{k}m$
• safety

  • suspended masses could fall and injure someone

  precautions

  • only pull down spring by a few cm and don't attach too heavy masses
• improvements

  • if spring moves horizontally, stop oscillation and start again
  • timing more oscillations reduces percentage uncertainty in period
  • fiducial marker should be at centre of oscillation so mass is moving past at fastest speed
  • there is the least uncertainty in stopping and starting the stopwatch
  • motion tracker and data logger find more accurate value for time period
  • eliminate random error in using stopwatch