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# 13.1.1 Shm Simple Pendulums

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### Transcript

• 1. 13.1.1 SHM Simple pendulum
• 2. Simple pendulum
• A pendulum consists of a small “bob” of mass m , suspended by a light inextensible thread of length l , from a fixed point
• We can ignore the mass of the thread
• The bob can be made to oscillate about point O in a vertical plane along the arc of a circle
• 3.
• We can show that oscillating simple pendulums exhibit SHM
• We need to show that a  x
• Consider the forces acting on the pendulum: weight , W of the bob and the tension , T in the thread
• We can resolve W into 2 components parallel and perpendicular to the thread:
• Parallel: the forces are in equilibrium
• Perpendicular: only one force acts, providing acceleration back towards O
• 4.
• 5.
• Parallel: F = mg cos 
• Perpendicular: F = restoring force towards O
• = mg sin 
• This is the accelerating force towards O
• F = ma  - mg sin  = ma (-ve since towards O)
• When  is small (>10 °) sin   
• Hence -mg = ma (remember  = s/r = x /l)
•  -mg ( x /l) = ma
• Rearranging: a = -g ( x /l) = pendulum equation
• (can also write this equation as a = - x (g/l) )
• 6.
• In SHM a  x
• Since g/l = constant we can assume a  x for small angles only
• SHM equation a = -(2  f ) 2 x
• Pendulum equation a = - x (g/l)
• Hence (2  f ) 2 = (g/l)
•  f = 1/2  (  g/l) remember T = 1/ f
• T = 2  (  l/g)
• The time period of a simple pendulum depends on length of thread and acceleration due to gravity
• 7. Measure acceleration of free fall using simple pendulums
• Use page 36 and 37 of “Physics by Experiment”
• 8.
• Set up the equipment and set the length of the string so T = 2s
• Mark a reference point on the stand (to count number of oscillations
• Displace the pendulum a few centimetres and release – the swing should be 1 plane
• As the pendulum passes the reference point start the stopwatch and measure the time for 20 oscillations
• Remember 1 oscillation is from O  A  O  B  O
• 9.
• Now change the length of the string (shorter or longer), measuring the length from the point of suspension to the centre of gravity of the bob
• Repeat the experiment
• Record results in a table with the column headings T, T 2 and y (in metres)
• Plot a graph T 2 against y – this should be a straight line graph
• 10. Analysis of results
• T = 2  (  l/g)
•  T 2 = 4  2 (l/g)
•  g = 4  2 (l/T 2 )