Looking for help with number 4 its a 2 part question. Thanks. 4. A mass m0 is su

Question

Looking for help with number 4 its a 2 part question. Thanks.

4. A mass m0 is suspended from a spring with spring constant k0. The mass is pulled down a distance of 5 centimeters from its equilibrium position and then released, so that it exhibits simple harmonic motion. The period of oscillation is 4 seconds. i. Suppose a second experiment has an identical spring, a mass 2m0(i.e.. twice the mass) and it is pulled down a distance of 12 centimeters from its equilibrium position and released. What is the period of oscillation for this experiment? Explain how you determined your answer. ii. A third experiment has a mass 2m0 and a spring constant 2k0. If this mass is pulled down 5 centimeters and released, what is period of oscillation? Explain your reasoning.

Explanation / Answer

time period of a spring = T = 2*pi*sqrt(m/k)

T = 4 s

(i)

mass m' = 2m

T' = 2*pi*sqrt(m'/k)

T' = 2*pi*sqrt(2m/k) = T*sqrt2 = 1.414*4 = 5.656 s

(ii)

T" = 2*pi*sqrt(m"/k") = 2*pi*sqrt(2m/2k) = T = 4 s

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