Vibrations experiments

Question 1

THE 2 PRACTICALS???!!??

Answer 1

1. Measurement of g with a Pendulum

2. Investigation of the Damping of a Spring

Question 2

Elaborate 1.
(The most important one)

Answer 2

• Period of oscillation of pendulum given by eqn:
• T = 2π√l/g…. also knowing what each letter represents
• Eqn rewritten as:
• T² = ((4π²)/g) x l
• Can be compared w/ eqn for straight line y = mm + c
• Hence, graph of T² against l
• should be straight line through origin
• w/ gradient of line = (4π²)/g
• Acceleration due to gravity determined from value of gradient
• and is equal to (4π²)/gradient

Extension:
- Used to measure height of a room, w/ known g
- T = 2π√(H-h)/g
- H = height of room, h = height above floor for pendulum

Question 3

Elaborate 2.
(And back to general)

Answer 3

• Relationship between amplitude of oscillation (A) and time (T) expressed by:
• A = A₀e^-λt
• … still knowing what each is: the 0 one = initial, λ = unknown constant
• Take logs:
• lnA = lnA₀ - λt
  ^^
• Compared w/ eqn for straight line y = mx + c
• Graph: lnA against t, gives straight line
• of gradient -λ and intercept lnA₀