A pendulum is set in motion. Consider what will happen to the frequency or perio

Question

A pendulum is set in motion. Consider what will happen to the frequency or period in each of the following situations.
Increase, Stay the same, or Decrease  If the mass of the pendulum is doubled, the period will _______.
Increase, Stay the same, or Decrease  If the length of the pendulum is cut in half, the period will _______.
Increase, Stay the same, or Decrease  If the length of the pendulum is doubled, the frequency will _______.
Increase, Stay the same, or Decrease  If the acceleration due to gravity is increased (suppose you travel to the surface of Jupiter), the period will _______.
Increase, Stay the same, or Decrease  If the amplitude of the motion is doubled, the period will ______.

Explanation / Answer

Period of pendulum is given by:

T = 2*pi*sqrt (L/g)

f = 1/T

Case 1

when mass is doubled

Since period does not depends onmass, it will

Stay the same

Case 2

L1 = L/2

Since period is directly proportional to square root of length, SO if length decreased, then period will also

Decrease

Case 3

L1 = 2*L

Since period is directly proportional to square root of length, SO if length increased, then period will also increase And we know that frequency is inversely proportional to period, SO if period increased, then frequency will

Decrease

Case 4

Since period is inversely proportional to square root of acceleration due to gravity, SO if 'g' increased, then period will

Decrease

Case 5.

Since period does not depends on Amplitude, So

Stay the same

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