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. If the mass of the pendulum is cut in half, the frequency will _______. If the amplitude of the motion is cut in half, the frequency will ______. If the acceleration due to gravity is increased (suppose you travel to the surface of Jupiter), the frequency will _______. If the length of the pendulum is cut in half, the frequency will _______. If the length of the pendulum is cut in half, the period will _______.

Explanation / Answer

time period T=(2pi)*sqrt(l/g)

and

frequency f=(1/2pi)*sqrt(g/l)

a)

If the mass of the pendulum is cut in half,

the frequency will be same,

because,

frequency does not depends on the mass

b)

If the amplitude of the motion is cut in half,

the frequency will be same

because,

frequency does not depends on the amplitude

c)

If the acceleration due to gravity is increased

the frequency will be increases

because,

frequency f=(1/2pi)*sqrt(g/l)

here if g increases then f increases

d)

If the length of the pendulum is cut in half,

the frequency will be increases

because,

frequency f=(1/2pi)*sqrt(g/l)

frequency f'=(1/2pi)*sqrt(g/(l/2))

f'=(1/2pi)*sqrt(2g/l)

f'=sqrt(2)*((1/2pi)*sqrt(g/l))

f'=sqrt(2)*f

e)

If the length of the pendulum is cut in half,

the period will be decreases,

because,

time period T=(2pi)*sqrt(l/g)

time period T'=(2pi)*sqrt((l/2)/g)

time period T'=T/sqrt(2)

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