Frequency:

$\overline{){\mathbf{f}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{T}}}$

The time period of the mass of a spring system is expressed as:

$\overline{){\mathbf{T}}{\mathbf{=}}{\mathbf{2}}{\mathbf{\pi}}\sqrt{\frac{\mathbf{m}}{\mathbf{k}}}}$

**Part A**

T_{A} = 4 s

f_{A} = 1/4 = 0.25 Hz

The frequency of system A is 0.25 Hz.

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.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Simple Harmonic Motion of Vertical Springs concept. You can view video lessons to learn Simple Harmonic Motion of Vertical Springs. Or if you need more Simple Harmonic Motion of Vertical Springs practice, you can also practice Simple Harmonic Motion of Vertical Springs practice problems.

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Based on our data, we think this problem is relevant for Professor DeJonghe's class at UIC.