![]() One such type of periodic motion is simple harmonic motion or SHM. We find the motion of these objects keeps repeating themselves. The frequency, in this case, is the reciprocal of the period.We see various types of motion in our day-to-day life, such as the motion of the blades of a fan, motion of the hands of a wristwatch, motion of the wheels of a car, etc. The period, T, is the time required for one cycle and the frequency, f, is the number of cycles that occur in exactly 1.00 second. One cycle refers to the complete to-and-fro motion that starts at some position, goes all the way to one side, then all the way to the other side, and returns to the original position. The greatest displacement of the mass from the equilibrium position is called the amplitude of the motion. ![]() Circular motion and simple harmonic motion have a lot in common. The movement of the light will appear to you to be back and forth in simple harmonic motion. You are sitting in a chair at some distance from the merry-go-round so that the only part of the system that is visible to you is the light bulb. Another example is to imagine a glowing light bulb riding a merry-go-round at night. It moves consistently from the far left to the far right until you stop spinning the yo-yo. The object will move back forth in the same way that a mass moves in SHM. Remember the yo-yo we spin over our heads? In your mind, turn the circle so that you are looking at it on edge imagine you are eight feet tall, and the yo-yo's circle is exactly at eye level. Imagine an object moving in uniform circular motion. In a frictionless system, the mass would oscillate forever, but in a real system, friction gradually reduces the motion until the mass returns to the equilibrium position and motion stops. Eventually, when the mass reaches its maximum displacement on this side of the equilibrium position, the velocity has returned to zero and the restoring force and acceleration have returned to the maximum. As the spring is stretched further, the displacement increases, the restoring force increases, the acceleration toward the equilibrium position increases, and the velocity decreases. Because of its inertia, the mass will continue past the equilibrium position, and stretch the string. The acceleration, therefore, is zero, but the mass is moving at its highest velocity. When the mass reaches the equilibrium position, there is no restoring force. As the mass moves toward the equilibrium position, the displacement decreases, so the restoring force decreases and the acceleration decreases. At the position of maximum displacement, the restoring force is at its greatest - the acceleration of the mass will be greatest. When the mass is at the maximum displacement position, velocity is zero because the mass is changing direction. The spring exerts a force on the mass pushing it toward the equilibrium position. Suppose the spring is compressed a distance x=A, and then released. ![]() This equation is accurate as long as the spring is not compressed to the point that the coils touch nor stretched beyond elasticity. The spring constant is represented by k and its units are N/m. In the equation above, the constant of proportionality is called the spring constant. (A spring must be chosen that obeys this requirement.) The magnitude of the restoring force, F, in either case must be directly proportional to the distance, x, the spring has been stretched or compressed. Similarly, if the object is pushed to the left, the spring will be compressed and will exert a restoring force to return the object to its original position. If the object is pulled to the right, the spring will be stretched and exert a restoring force to return to the weight to the equilibrium position. This position is the middle, where the spring is not exerting any force either to the left or to the right. The position shown in the illustration is the equilibrium position. The spring is considered to be weightless. The surface supports the object so its weight (the force of gravity) doesn’t get involved in the forces. This motion is also known as simple harmonic motion, often denoted as SHM.Ī useful design for examining SHM is an object attached to the end of a spring and laid on a surface. When we speak of a vibration or oscillation, we mean the motion of an object that repeats itself, back and forth, over the same path. Many objects vibrate or oscillate – an object on the end of a spring, a tuning fork, the balance wheel of a watch, a pendulum, the strings of a guitar or a piano.
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