The two graphs in (Figure 1) are for two different vertical mass/spring systems.

Question

The two graphs in (Figure 1) are for two different vertical mass/spring systems.

Part A

What is the frequency of system A?

Express your answer using two significant figures.

Part B

What is the first time at which the mass of system A has maximum speed while traveling in the upward direction?

Express your answer using two significant figures.

Part C

What is the period of system B?

Express your answer using two significant figures.

Part D

What is the first time at which the mechanical energy of system B is all potential?

Express your answer using two significant figures.

Part E

If both systems have the same mass, what is the ratio kA/kB of their spring constants?

Express your answer using two significant figures.

Explanation / Answer

A) frequency = 3/12 = 0.25 Hz

B) At t = 3T/4 = 3/(4*0.25) = 3 sec

C) period = 12/2 = 6 sec

D) t = T/4 = 6/4 = 1.5 sec

E) f = sqrt(k/m)/(2*pi)

=> f1/f2 = sqrt(k1/k2)

=> ka/kb = 0.25*0.25/(0.16*0.16) = 2.44 Answer

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