Phy 122L/Phy 132L
Pre-Lab: Simple Harmonic Motion
Name:
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Choose the best answer. See lab manual for definitions of variables used.
(10 pts; 2 pages)
1. Why is there a negative in F = -kx (Hookes’s law)? (Answer in a single sentence only!)
2. What are the units of “k”, the spring constant? (Use SI units.)
a. kg/s2 b. N
c. N/m
d. kg
e. Choices a & c are both correct
Remember in physics, when we say plot C vs D, we mean that C is on the “y” or vertical
axis and D is on the “x” or horizontal axis of your graph. This will help you answer
questions 3, 5, 7, 8, 9 and 10 in this prelab, and questions on other prelabs, lab reports, and
the lab final exam.
3. In part A, you will make a series of measurements of elongation distance, x, due to suspended
mass, M, for a spring in static equilibrium (not oscillating), and plot Mg vs. x. (where g is the
acceleration due to gravity). What are the (SI) units of the slope of the plot?
a. kg
b. N/m
c. N
d. kg/s2
e. m
f. Choices b & d are both correct
Questions 4-8: In part B, you will determine the period of oscillation, T, for different
values of suspended mass, m, on an oscillating spring, and plot T2 vs. m.
4. How should the average period, T, be calculated? (Hint: the SI unit of period is seconds.)
a. number of oscillations/total time
b. total time/number of oscillations
c. T = 30
5. What are the (SI) units of the slope of the plot (T2 vs. m)?
a. s2
b. s2/kg
c. kg/s2
d. N/m
e. kg
f. Choices c and d are both correct
6. In equation 2 in the lab manual, m is the effective mass of the oscillating system, not the
suspended mass. Part B procedure uses m to represent the suspended mass. I will use me to
represent the effective mass of the system to minimize confusion. According to the lab
manual, what is the effective mass approximately equal to for a coil spring?
a. the mass of the spring
b. 1/3 mass of the spring
c. 1/3 mass of the spring plus the suspended mass
d. the suspended mass
7. What are the (SI) units of the x-intercept (where T2 = 0) of the plot of T2 vs. m?
a. s2
b. s2/kg
c. kg/s2
d. 1/s2
e. kg
CSU Pomona
Updated 4/07/15
Dr. Julie J. Nazareth
Phy 122L/132L
Pre-Lab: Simple Harmonic Motion
8. According to the part B procedure, what should the x-intercept (where T2 = 0) be equal to?
a. the mass of the spring, ms
b. 1/3 mass of the spring, mo
c. 1/3 mass of the spring plus the suspended mass, me = mo + m
d. negative 1/3 mass of the spring, -mo
e. the suspended mass, m
The following helps you to answer questions 9-10. (Note: you will be using this technique
almost every week to solve for values from the results of your graph(s).)
me
In equation 2 of the lab manual, we are given T = 2π
. Note that I have labeled the mass
k
under the square root as me, for effective mass, to distinguish it from m, the suspended mass
(mass hung off the end of the spring). The effective mass of the spring, me, is the suspended
mass, m, plus the mass of the oscillating part of the spring, mo, or me = m + mo. If you plot T2 vs
m (period squared versus suspended mass), how can you solve for the spring constant? You can
calculate it using the slope, but it is not equal to the slope. Start with the theoretical
relationship/formula, and rearrange it using algebra so that T2 is on the left hand side and m on
the right hand side. Then compare your rearranged equation to the equation of a straight line. I
will show you most of the steps below and you finish it off
Squaring both sides gives
T2 = 4π2 (me/k).
Substituting me = m + mo, gives
T2 = (4π2/k) m + (4π2/k) mo.
Compare this to the equation of a straight line:
“y” = slope “x” + y-intercept.
So the T2 values are plotted on the y (or vertical) axis of the graph (“y” = T2), the m values
are plotted on the x (or horizontal) axis (“x” = m), and the y-intercept is equal to (4π2/k) mo.
9. What is the slope of a graph of T2 vs m equal to symbolically (and I don’t mean T2/m)?
slope =
10. Take your result from question 9 and rearrange it algebraically to solve for k. Treat the word
slope as a single variable.
k=
CSU Pomona
Updated 4/07/15
Dr. Julie J. Nazareth