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In a labratory experiment, a student measured the period of a swing for a 1 -kg pendulum for varing lengths, as shown below.

Length (m) Period (s)
0.05 0.30
0.20 0.90
0.40 1.30
0.60 1.60
0.80 1.80
1.00 2.00

a.) Deterine the period of a pendulm whose length is 0.25 m.

b.) Now the bob is removed from the pendulum and placed on a spring to form a mass-spring system. What would the spring constant of the spring have to be in order to have the same period as that of the pendulum in part a?

a) Plot a graph of Period (P) vs Length (L) and interpolate. If you plot P vs sqrt L, You should get a very straight line, which will make it easier to accurately interpolate the value of P for L = 0.25 m.

("sqrt" means "square root of").

b) Assume you are trying to match the period for a L = 0.25 m pendulum. Get the value of that period from (a). The, for a spring, set

P = 2 pi sqrt (m/k)

Solve for the spring constant, k.

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  1. A helical spring is 59 cm long when a load of 100 N is hung from it and 62 cm long when the load is 120 N. Find its spring constant.

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