RP: Investigating SHM

• What is the resolution of the stopwatch used in the experiment?

  ±0.01 s
• What is the resolution of the metre ruler used in the experiment?

  ±1 mm
• What is the aim of the mass-spring system experiment?

  To calculate the spring constant of a spring
• How does the time period of oscillations vary in the mass-spring system experiment?

  It varies with the mass
• What are the independent and dependent variables in the mass-spring system experiment?

  • Independent variable: mass, m
  • Dependent variable: time period, T
• What are the control variables in the mass-spring system experiment?

  • Spring constant, k
  • Number of oscillations
• What is the first step in the method for the mass-spring system experiment?

  Set up the apparatus without additional masses
• How far should the mass hanger be pulled down before letting go?

  Between 2−5 cm
• When should the stopwatch be started in the mass-spring system experiment?

  When it passes the nail marker
• How is the time period calculated after recording the time for 10 oscillations?

  Divide the time by 10

  
• What should be done after adding a 50 g mass to the holder?

  Repeat the procedure for 8−10 readings
• What is the equation for the time period of a mass-spring system?

  • T = time period (s)
  • m = mass (kg)
  • k = spring constant (N m^-1)

  
• What happens when both sides of the time period equation are squared?

  It allows comparison to a straight line equation
• What does the gradient of the graph of T against m represent?

  Gradient = $\frac{4\pi}{k}$

  
• What is the relationship between T and m in the graph?

  T and m are directly proportional
• How can the spring constant be compared to Hooke's law?

  • k is found from the gradient of a force F vs. extension x graph
• What is the aim of the simple pendulum experiment?

  To calculate the acceleration due to gravity
• What are the independent and dependent variables in the simple pendulum experiment?

  • Independent variable: length, L
  • Dependent variable: time period, T
• What are the control variables in the simple pendulum experiment?

  • Mass of pendulum bob, m
  • Number of oscillations
• What is the first step in the method for the simple pendulum experiment?

  Set up the apparatus with length at 0.2 m
• How should the pendulum be positioned before starting the experiment?

  Hang vertically downwards at equilibrium
• When should the stopwatch be started in the simple pendulum experiment?

  When the pendulum passes the needle marker
• How is the time period calculated after recording the time for 10 oscillations in the pendulum experiment?

  Divide the time by 10

  
• What should be done after adjusting the length of the pendulum?

  Repeat the procedure for 8−10 readings
• What is the equation for the time period of a simple pendulum?

  • T = time period (s)
  • L = length of the pendulum (m)
  • g = acceleration due to gravity (m s^-2)
• What happens when both sides of the time period equation for the pendulum are squared?

  It allows comparison to a straight line equation
• What does the gradient of the graph of T against L represent?

  Gradient = $\frac{4\pi}{g}$

  
• What is the relationship between T and L in the graph?

  T and L are directly proportional
• How can the acceleration due to gravity be evaluated?

  • Compare obtained value of g to accepted value: g = 9.81 m s^-2
• What are the systematic and random errors in the experiments?

  Systematic Errors:

  • Reduce parallax error by eye level viewing

  
  

  Random Errors:

  • Record time for 10 oscillations
  • Keep amplitudes small for accuracy
• What safety considerations should be taken during the experiments?

  • Place soft surface below equipment
  • Limit pull distance for mass-spring system
  • Clamp wooden blocks tightly
• What is the first step in calculating the spring constant from the experiment results?

  Complete the table and calculate T
• What should be done after plotting the graph of T against m?

  Calculate the gradient of the graph
• How is the gradient calculated from the graph?

  Gradient = $\frac{0.84 - 0.42}{0.4 - 0.06}$

  
• How is the spring constant, k, calculated from the gradient?

  k = $\frac{4\pi^2}{\text{gradient}}$

  
• What is the final calculated value of the spring constant, k?

  32.0 N m^-1