A meterstick is clamped to a table at the left end at about 90.0cm. when a mass

Question

A meterstick is clamped to a table at the left end at about 90.0cm. when a mass is taped to the end, the stick bends like a spring, and displaces downward a distance Ay. F(spring) F(gravity) The two forces acting on the mass are, mg downward, and kAy which pushes upward with an equal amount of force if the mass is in equilibrium. We can use a measurement of the mass and displacement to determine the spring constant, k. If we now jostle the mass, it will oscillate up and down. The oscillation period can be measured by counting and timing several oscillations (experiment). We also have a theoretical expression for the system that gives us the time period "T". For a mass on a spring system: spring 2n A pendulum with a mass hanging at the end of a string of length L behaves in a similar manner, but the oscillation period for the pendulum is given by: Pendulum 27t 1. Consider a system like the meterstick spring described above Place a 500 the the end and observe mass to displace 12.0cmt0.5cm down. What is spring constant (give uncertainty also) and theoretical time constant for the mass on a spring system

Explanation / Answer

1)

spring constant K = sqrt(mg/dy)

K = sqrt(500*10^-3*9.8/0.12)

K = 6.4 N/m

time constant T = 2pi*sqrt(m/k) = 2*pi*sqrt(dy/g)

Tspring = 2*pi*sqrt(0.12/9.8) = 0.695 s

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2)

measured time period T = 14/20 = 0.7 s

measures time period > theoretical time constant

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3)

Tpendulum = 2*pi*sqrt(L/g)

Tpendulum = 2*pi*sqrt(1.5/9.8) = 2.46 s

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