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posted by  Chrissy0022 on 11/5/2009 2:31:21 AM  |  status: Live  |  Earned Karma: 404

spring is hanging vertically

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

1.      A spring is hanging vertically in an unstretched condition.  The spring stretches

      20 cm when a 500 g mass is hung from it.  The spring is then stretched an additional

      40 cm from this equilibrium point and released.

a.       A.What is the spring constant?

b.      B.What is the amplitude of the oscillation?

c.       C.What is the angular frequency of the oscillation?

d.      D.What is the maximum velocity?

e.       What is the magnitude of the maximum acceleration of the mass?
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posted by jerry2009 on 11/5/2009 2:41:50 AM  |  status: Live
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Response Details:

    Mass suspended, M = 0.5 kg

(a)

   Spring constant , K = M g / x  ( where x = extension )
                                  = 0.5 * 9.8 / 0.2
                                  = 24.5 N / m

(b)

    Amplitude, A = 60 cm = 0.6 m

(c)

    Angular frequency, ω = √ ( K / M )
                                     = √ ( 24.5 / 0.5 )
                                     = 7 rad / s

(d)

    Max Velocity, Vmax = ω A
                                    = 7 * 0.6  
                                    = 4.2 m / s

(e)

    max acceleration, a max = ω2 A
                                        = 72 * 0.6
                                        = 29.4 m / s2
                                       

   

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