Practical 4 - Investigaton of the damping of a spring

Question 1

What is this practical an example of?

Answer 1

Exponential decay

Question 2

What is the damping of an oscillation spring an example of?

Answer 2

Exponential decay

Question 3

Which relationship does the exponential decay of the damping of an oscillating spring follow?

Answer 3

A = Aoe^-kt

Question 4

A

Answer 4

Amplitude at time t

Question 5

Ao

Answer 5

The initial amplitude a time t=0

Question 6

k

Answer 6

Decay constant of the system

Question 7

How is the technology of the trolley used in this practical?

Answer 7

The trolley has a position sensor which logs the position along with time

Question 8

Interval between samples

Answer 8

0.05s

Question 9

Method

Answer 9

1.) the logger is started and the trolley send into oscillation
2.) data is collected until the amplitude has fallen from 0.13cm to 0.02cm
3.) data is sampled from the collected data to provide sufficient points to plot

Question 10

Equation for taking logs of A=Aoe^-kt

Answer 10

Ln (A) = ln (Aoe^-kt) = In (Ao) + In(e^-kt)
Ln (A) = ln (Ao) - kt

Question 11

y-axis of graph

Answer 11

Ln (A)

Question 12

Y-intercept of graph

Answer 12

Ln (Ao)

Question 13

Gradient of graph

Answer 13

k (decay constant)

Question 14

x-axis of graph

Answer 14

Time

Question 15

Units of ln (A)

Answer 15

No units (logs don’t have units)

Question 16

How can we check our answer?

Answer 16

Find the amplitude at t=10s and input into the equation
Check for agreement

Question 17

What’s another method for this practical?

Answer 17

Set up a spring on a stand with a cardboard disc to increase air resistance with a mass on the bottom. Measure the amplitude with a ruler