1.) A 0.25-kilogram mass on a vertical spring oscillates at a frequency of 2.0 H

Question

1.) A 0.25-kilogram mass on a vertical spring oscillates at a frequency of 2.0 Hz. If a 0.60-kilogram mass were instead suspended from the same spring, what would be the frequency of oscillation?

2.) A 0.50-kilogram mass oscillates in simple harmonic motion on a spring with a spring constant of 260 N/m. What is the frequency of the oscillation?

3.) A breeze sets in oscillation a lamp suspended from the ceiling. If the period is 2.6 s, what is the distance from the ceiling to the lamp at the lowest point? Assume the lamp acts as a simple pendulum.

Explanation / Answer

1) w = sqrt(k/m)

so w2/w1 = sqrt(m1/m2)

so f1 = 2*sqrt(0.25/0.6)= 1.29 Hz

2) f = (1/2pi) sqrt(k/m) = 1/(2*pi)*sqrt(260/0.5)=3.63 Hz

3) T = 2 pi sqrt(L/g)

L = g*(T/(2 pi))^2 = 9.81*(2.6/(2*pi))^2=1.68 s

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