Physics Laboratory Experiments
8th Edition
ISBN: 9781285738567
Author: Jerry D. Wilson, Cecilia A. Hernández-Hall
Publisher: Cengage Learning
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Question
Chapter 4, Problem 2EP
To determine
The physical parameters that can be varied in the simple pendulum arrangement.
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If you did the previous question right, you hopefully got an expression for yo. You may notice that
you can simplify the differential equation a little bit:
d'y
k
(y – yo)
dt2
т
The parameter yo now plays the roll of the "relaxed length". A better term may be "equilibrium value
for y". But mathematically, it's identical to a relaxed length with the spring as the only force. We
continue using this equation:
y(t) = Y0 + A cos(wt + y)
Now, solve for A (in cm) with these parameters. Again, if you need more information, enter
-100000. The parameters are:
•m = 200 grams
• Yo = (equilibrium value) = 40 cm
• k = (spring constant) = 0.03 N/cm
Our unforced spring mass model is mx00 + βx0 + kx = 0 with m, β, k >0. We know physically that our spring will eventually come to rest nomatter the initial conditions or the values of m, β, or k. If our modelis a good model, all solutions x(t) should approach 0 as t → ∞. Foreach of the three cases below, explain how we know that both rootsr1,2 =−β ± Sqrt(β^2 − 4km)/2mwill lead to solutions that exhibit exponentialdecay.(a) β^2 − 4km > 0.
(b) β^2 − 4km =0.
(c) β^2 − 4km >= 0.
Chapter 4 Solutions
Physics Laboratory Experiments
Ch. 4 - Scientists use models and theories to describe...Ch. 4 - Prob. 2EPCh. 4 - Prob. 3EPCh. 4 - The mass (m) of the pendulum bob may be varied....Ch. 4 - Check with one of your fellow students (or your...Ch. 4 - Describe what is meant by the scientific method...Ch. 4 - What are the physical parameters in the...Ch. 4 - Prob. 3ASACh. 4 - How does the period of a pendulum vary...Ch. 4 - How will you experimentally check the theoretical...
Ch. 4 - Prob. 6ASACh. 4 - How can the parabolic form y = ax2 be plotted as a...Ch. 4 - What is meant by damped harmonic motion, and what...Ch. 4 - It was suggested that you measure the time for...Ch. 4 - Prob. 2QCh. 4 - Prob. 3QCh. 4 - Prob. 4QCh. 4 - Prob. 5QCh. 4 - Suppose in the damped equation had ek1t and ek2t,...Ch. 4 - Prob. 7Q
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- Please answer this, I need help.arrow_forwardProblems 5 & 6 refer to the mass-spring oscillator depicted in the figure on the right. The block has a mass of 350 g, and is attached to a spring with a spring constant of k pushed 20 cm to left from C, its equilibrium position, before being released and allowed to move horizon- tally on a frictionless surface. . Ax = 20 cm 45 N. The mass is initially m A B DE 5. What is the frequency of oscillation for the block? A. 0.13 Hz В. 0.35 Hz С. 1.8 Hz D. 7.8 Hz 5. 6. What is the speed of the block as it passes point B? A. 0.50 m/s В. 1.0 m/s C. 1.5 m/s D. 2.0 m/s 6.arrow_forwardDraw a diagramarrow_forward
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