AMPLITUDE, TIME-PERIOD AND FREQUENCY OF VIBRATION PRACTICE PROBLEM

 

Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point

Amplitude: the maximum displacement of a wave from its undisturbed ( equilibrium) position

Frequency: the number of waves passing a given point in a second

Frequency is the inverse of the wave’s time period

Period:  time for a particle on a medium to make one complete vibrational cycle

Formula:

Question no. 1

The time needed to complete 300 vibrations is 1 minute. Calculate :

a.      Its time-Period  

b.     Its frequency

Answer :

a.      T = t : n

     T = 60s : 300 = 0.2 s

b.     f = n : t

f = 300 : 60 = 5 Hz

Question no. 2

An object vibrates 100 times  in  25 s. Calculate :

a.      Its time-Period  

b.     Its frequency

Answer :

a.      T = t : n

     T = 25s : 100 = 0.25 s

b.     f = n : t

f = 100 : 25 = 4 Hz

Question no. 3

An object vibrates 100 times  in  25 s. How many vibrations will happen in 2 minutes?

Answer :

T₁ = T₂

t₁ : n₁ = t₂ : n₂

25 s : 100 = 120 : n₂

n₂ = 4 x 120 = 480 times

Question no. 4

An object vibrates 120 times  in  1 minute. How many vibrations will happen in 2 hours?

Answer :

T₁ = T₂

t₁ : n₁ = t₂ : n₂

1 minute : 100 = 120 minutes : n₂

n₂ = 100 x 120 = 12000 times

Question no. 5

Look at the figure below.

The distance from A to C is 6 cm. the time needed from A to C is 0.4 second. Calculate :

a.      its amplitude

b.     its time-period

c.      its frequency

Answer:

a.      Amplitude = distance A-B

                  = 6 cm : 2 = 3 cm

b.     T = t : n = 0.4 s : 0.5 = 0.8 s

c.      f = n : t = 0.5 : 0.4s = 1.25 Hz

Question no. 6

Look at the figure below!

a.      which pendulum above has the greatest time-period?

b.     which pendulum above has the greatest frequency?

Answer :

a.      The greatest time-period : figure S

b.     The greatest frequency: figure P