College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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If you drive an old, run-down car, and every time you hit the brakes the front of the car bounces up and down several times, how would you characterize the damping of the springs?
a.Underdamped
b. Overdamped
c. Critically damped
d. Naturally damped
e. Resonantly damped
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- I would like some help with thus problem, thank you!arrow_forward1: In this question we will study the damped harmonic oscillator. Consider the following spring-mass system. kr bà Figure 1: Spring-mass system with a friction force. That is, an object of mass m is attached at the end of a spring with spring-constant k. We will also consider the effect of friction. Friction works in the opposite direction of motion, as illustrated in the figure. A) Show that the differential equation governing the damped spring-mass system is: më = -bå – kx (1) dr and i = dt where i = dt2 b) To solve the differential equation (1), we will take the following ansatz: r(t) = Ae. (2) If the above r(t) is a solution of Eq. (1) show that A has to satisfy the following equation: 1² +27d + wi = 0, (3) * and wi = k Solve the above equation to find A. m2 b where y 3= 2m c) For wi >?, show that the general solution can be written as: x(a) = Ae-t cos (wt +0) (4) where w? = w - 7². 2: Using Fermat's principle prove the law of reflection and the law of refraction of light.arrow_forwardThe period of oscillation of a mass-spring system: 1. Depends on the amplitude. 2.Depends on the ratio of amplitude and the mass. 3. Depends on the mass.arrow_forward
- A 4.0-kg block executes simple harmonic motion according to the following equation for the position as a function of time: x(t) = (0.60 m)cos(5t) What is the mechanical energy of the oscillator? a. 18 J b. 22 J c. 20 J d. 16 J e. 14 Jarrow_forwardA mass on a spring oscillates with an amplitude 0.12 m and a period of 1.0 s. What will be the acceleration of the mass at t = 0.50s? A) 4.7 m/s² B) -4.7 m/s² C) 0.12 m/s² D) 0 m/s?arrow_forwardYou attach a 2.0 kgkg object to a spring, pull it down 0.16 mm from the equilibrium position, and let it vibrate. You find that it takes 4.6 ss for the object to complete 10 vibrations. Determine the frequency of vibrations. Determine the spring constant. Determine the total energy of system Determine the maximum speed. Determine the maximum accelerationarrow_forward
- Two children are on adjacent swings at the playground. One child has twice the mass of the other child. Will they be able to swing in sync with the other child? A. No, this is impossible because the mass of the two are different. B. No, this is impossible because the gravity is unknown. C. Yes, as long as the lengths of the two swings are proportional to the mass. D. Yes, as long as the lengths of the swings are the same.arrow_forwardThe next few questions challenge you to figure out the acceleration due to gravity ( g ) on various hypothetical alien planets. On Planet #1, you drop a stone from rest, 63.8 m above the ground, and the stone hits the ground 3.88 s later. What is the value of g on Planet #1? 16.44 m/s^2 32.89 m/s^2 8.48 m/s^2 4.24 m/s^2arrow_forward7. In a lab experiment, you are given a spring with a spring constant of 14 N/m. What mass would you suspend on the spring to have an oscillation period of 0.93 s when in SHM? kgarrow_forward
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