Part A If a pendulum has a period T and you quadruple its length, what is its ne

Question

Part A

If a pendulum has a period T and you quadruple its length, what is its new period in terms of T?

B.

IF a pendulum has a length L and you want to double its frequency, what should be its length in terms of L?

C.

Suppose a pendulum has a length L and period T on earth. If you take it to a planet where the acceleration of freely falling objects is twenty times what it is on earth, what should you do to the length to keep the period the same as on earth?

D.

If you do not change the pendulums length in part (c), what is its period on that planet in terms of T?

E.

If a pendulum has a period T and you double the mass of its bob, what happens to the period (in terms of T)?

Explanation / Answer

T = 2pi*sqrt(L/g)

part a )

L' = 4L

T' = 2pi*2* sqrt(L/g)

T' =2T

part b )

f = 1/2pi * sqrt(g/L)

2f/f = sqrt(L/L')

4 = L/L'

L' = L/4

part c )

T = 2pi*sqrt(L/g)

T = 2pi*sqrt(L'/20g)

1 = sqrt(20/L')

L' = 20L

part D )

T' = 2pi*sqrt(L/20g)

T' = 0.2236 T

part e )

period does not depend on mass so period is unchanged

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