link for activity homework

https://phet.colorado.edu/sims/html/masses-and-springs/latest/masses-and-springs_en.html

Show one sample calculation

Table 1: Finding values of k
mass used (kg)	Displacement from natural length (m)	g (N/kg)	k (N/m)
0.08	0.048 m	9.8
0.1	0.048m	9.8
0.120	0.048m	9.8
0.140	0.048m	9.8
0.160	0.048m	9.8

Values of X for each sections is

0.02

0.025

0.03

0.035

0.04

Part 2: Finding the relationship between k, attached mass, and period.

Now, set damping to None. Release a mass from the natural length. Try to be as close as possible to the natural length. You should barely see the displacement arrow if at all.

To measure the period, you can use your phone/other timer or use the built-in timing device. You can be more accurate if you do either or both of the following:

Set the speed to slow, making sure to use the built-in timing device that slows down alongside with the slow setting

Measure the time it takes to make 10 up-down motions and then divide by 10 (or whatever number you so choose)

How does the value of k and m affect the period of motion? Try it with three different masses and five different values of k. The first mass should have mass x, second 2x, and third 4x. Replace these with the masses you used. The k values are measured from the previous part.

Before doing any measurements of the period, answer the following questions:

Do you think increasing k while keeping the same mass will increase or decrease the period? Explain your answer.

Do you think increasing mass while keeping the same k will increase or decrease the period? Explain your answer.

Put the values of K for each that was found at the sections above. then find a time

Table 2: Periods of up-and-down motion
k (N/m)	period with mass x (seconds)	period with mass 2x (seconds)	period with mass 4x (seconds)

Graph period (y-axis) vs k (x-axis), three masses on the same grid. Have some sort of legend for the points so you know which value is which mass. Do not connect the dots.

Answer the following discussion questions. Explain your answers with specific examples

When you double the mass, by what factor does the period change? Try with a few different value pairs. Does this round to a whole number?

When you quadruple the mass, by what factor does the period change? Try with a few different value pairs. Does this round to a whole number?

From the previous two questions, what seems to be the general mathematical relationship between the attached mass and the period of up-down-motion?

Test your hypothesis from the previous question with another pair of masses for any one value of k, this time with a mass of 3x. Compare that period to the period for a mass of x. Is your hypothesis correct? Explain.

Do the same analysis as above but with k, for two different factors. This would be approximate since your values of k are calculated from your measurements.

For example: if k = 50, T = 20 and k = 150, T = 5: We can say when k increases by a factor of 3 (50*3=150), the period decreases by a factor of 4 (20/4=5) . Pick ones that were consistent between the three masses.

From the analysis of your graph and from the previous question, what seems to be the relationship between the value of k and the period? Explain using the types of functions and relations you have seen in math class.

Name two variables we kept constant during this activity that may affect the relationship between period, k, and mass, if we added that variable. Briefly explain how you could determine the contribution of those variables to the period of the mass's motion.

Answer the following calculation questions. Show your work.

Be very careful with when you use force F = kx and when you use energy E = 1/2kx^2

Consider a spring of k = 49 with damping = 0. A mass of 0.60kg is attached to the spring and released from the natural length. Throughout the simple harmonic motion of the mass, the mass experiences two forces, a force from the spring up and gravity down.

Calculate the acceleration of the mass (including direction) just as it is released. Remember that at this position, the stretch of the spring is zero.

How far below the natural length will the spring stretch before rebounding back up? At this position, the speed of the mass is momentarily zero.

At this bottommost position, calculate acceleration of the mass (including direction).

At some position during the motion of the mass, its net force and acceleration are equal to zero. How far below the natural length of the spring is this position?

At that position with zero net force, calculate the speed of the mass.

At what positions during the motion of the mass is its acceleration upwards? At what positions during the motion of the mass is its acceleration downwards? Explain.