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posted by  Chrissy0022 on 11/5/2009 2:37:03 AM  |  status: Live  |  Earned Karma: 404

mass on a string oscillates

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General Physics N/A N/A N/A 11/5/2009 at 1:00:00 PM
Question Details:

1.      A mass on a string of unknown length oscillates as a pendulum with a period of 6.0 s.  What is the period if:

a.       A.The mass is doubled?

b.      B.The string length is doubled?

c.       C.The string length is halved?

d.      D.The amplitude is doubled?
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posted by jerry2009 on 11/5/2009 2:53:00 AM  |  status: Live
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Response Details:

    Time period, T = 6 s

    Time period, T = 2 π √ ( L / g )            ( where L = length of the string and g = acceleration due to gravity )

(a)

    Time period is independent of the mass. Hence, it remains same.

    New Time period, T' = 6 s

(b)

    Time period is directly proportional to the square root of the length

          T  α  √ L

          T' / T = √ ( L' / L ) = √2

    New Time period, T' = √2 T = 6 √2 s = 8.49 s

(c)

    Time period is directly proportional to the square root of the length

          T  α  √ L

          T' / T = √ ( L' / L ) = 1 / √2

    New Time period, T' =  T / √2  = 6  / √2 s = 4.24 s
   

(d)


    Time period of the pendulum is independent of the amplitude   
   
    Time period , T' = 6 s
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posted by Mobiusdick on 11/5/2009 2:54:16 AM  |  status: Live
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Response Details:
Equation:  T = 2π√(l/g)

a) the mass has no impact on a pendulum.

b) Tb = 2π√(2l/g) => (√2)(2π√(l/g)) => √2 T0 => 6√2

c) Tc = 2π√(l/2g) => (1/√2)(2π√(l/g)) => 1/√2 T0 => 6/√2

d) Amplitude also has no impact on a pendulum.
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