Solved examples on SHM
Frequently Asked Questions
Ans: the energy quantities E, K, and U at x = 0, x = ±A/2, and x = ±A. Figure 14.15 is a graphical display of Eq. (14.21); energy (kinetic, potential, and total) is plotted vertically and the coordinate x is plotted horizontally. The parabolic curve in Fig. 14.15a represents the potential energy U = 1/2 kx2 . The horizontal line represents the total mechanical energy E, which is constant and does not vary with x. view more..
Ans: We can learn even more about simple harmonic motion by using energy considerations. The only horizontal force on the body in SHM in Figs. 14.2 and 14.13 is the conservative force exerted by an ideal spring. The vertical forces do no work, so the total mechanical energy of the system is conserved. We also assume that the mass of the spring itself is negligible. view more..
Ans: We still need to find the displacement x as a function of time for a harmonic oscillator. Equation (14.4) for a body in SHM along the x-axis is identical to Eq. (14.8) for the x-coordinate of the reference point in uniform circular motion with constant angular speed v = 2k/m view more..
Ans: PROBLEM SOLVING STRATEGY ON ENERGY MOMENTUM OF SHM view more..
Ans: So far, we’ve looked at a grand total of one situation in which simple harmonic motion (SHM) occurs: a body attached to an ideal horizontal spring. But SHM can occur in any system in which there is a restoring force that is directly proportional to the displacement from equilibrium, as given by Eq. (14.3), Fx = -kx view more..
Ans: A mechanical watch keeps time based on the oscillations of a balance wheel (Fig. 14.19). The wheel has a moment of inertia I about its axis. A coil spring exerts a restoring torque tz that is proportional to the angular displacement u from the equilibrium position. We write tz = -ku, where k (the Greek letter kappa) is a constant called the torsion constant. Using the rotational analog of Newton’s second law for a rigid body, gtz = Iaz = I d2 u>dt2 view more..
Ans: The following discussion of the vibrations of molecules uses the binomial theorem. If you aren’t familiar with this theorem, you should read about it in the appropriate section of a math textbook. view more..
Ans: A simple pendulum is an idealized model consisting of a point mass suspended by a massless, unstretchable string. When the point mass is pulled to one side of its straight-down equilibrium position and released, it oscillates about the equilibrium position. view more..
Ans: A physical pendulum is any real pendulum that uses an extended body, as contrasted to the idealized simple pendulum with all of its mass concentrated at a point. F view more..
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