Introduction To Simple Harmonic Motion Stretched The The Block Is Displaced D To The Right And When It Is Released A 1 (110.94 KiB) Viewed 31 times
+ Introduction to Simple Harmonic Motion stretched, the the block is displaced d to the right and when it is released, a force Consider the system shown in the figure. (Figure 1) It consists of a block of mass m attached to a spring of negligible mass and force constant k. The block is free to move on a frictionless horizontal surface, while the left end of the spring is held fixed. When the spring is neither compressed nor stretched, the block is in equilibrium. If the spring is acts on on it to pull it back toward equilibrium. By the time the block has returned to the equilibrium position, it has picked up some kinetic energy, so it overshoots, stopping somewhere on the other side, where it is again pulled back toward equilibrium. As a result, the block moves back and forth from one side of the equilibrium position to the other, undergoing oscillations. Since we are ignoring friction (a good approximation to many cases), the mechanical energy of the system is conserved and the oscillations repeat themselves over and over. The motion that we have just described is typical of most systems when they are displaced from equilibrium and experience a restoring force that tends to bring them back to their equilibrium position. The resulting oscillations take the name of periodic motion. An important example of periodic motion is simple harmonic motion (SHM) and we will use the mass-spring system described here to introduce some of its properties. Figure < 1 of 2 www wwm Item 2 Review | Constants Part A Which of the following statements best describes the characteristic of the restoring force in the spring-mass system described in the introduction? ► View Available Hint(s) The restoring force is constant. The restoring force is directly proportional to the displacement of the block. The restoring force is proportional to the mass of the block. O The restoring force is maximum when the block is in the equilibrium position. Submit Part B As shown in the figure(Figure 2), a coordinate system with the origin at the equilibrium position is chosen so that the x coordinate represents the displacement from the equilibrium position. (The positive direction is to the right.) What is the initial acceleration of the block, ao, when the block is released at a distance A to the right from its equilibrium position? Express your answer in terms of some or all of the variables A, m, and k. ▸ View Available Hint(s) ΠΙ ΑΣΦ ? ao = Submit Part C
Part C What is the acceleration ₁ of the block when it passes through its equilibrium position? Express your answer in terms of some or all of the variables A, m, and k. ▸ View Available Hint(s) IVE ΑΣΦ ? a₁ = Submit Part D Complete previous part(s) Using the information found so far, select the correct phrases to complete the following statements. Part E The magnitude of the block's acceleration reaches its maximum value when the block is ▸ View Available Hint(s) O in the equilibrium position. at either its rightmost or leftmost position. O between its rightmost position and the equilibrium position. between its leftmost position and the equilibrium position. Submit
Part F The speed of the block is zero when it is ▸ View Available Hint(s) in the equilibrium position. at either its rightmost or leftmost position. between its rightmost position and the equilibrium position. between its leftmost position and the equilibrium position. Submit Part G The speed of the block reaches its maximum value when the block is ▸ View Available Hint(s) in the equilibrium position. at either its rightmost or leftmost position. between the rightmost position and the equilibrium position. between the leftmost position and the equilibrium position. Submit
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