Let’s begin with a straightforward example of simple harmonic motion (SHM). A spring is mounted horizontally on an air track as in (Figure 1), with the left end held stationary. We attach a spring balance to the free end of the spring, pull toward the right, and measure the elongation. We determine that the stretching force is proportional to the displacement and that a force of 6.0 NN causes an elongation of 0.030 mm. We remove the spring balance and attach a 0.50 kgkg object to the end, pull it a distance of 0.040 mm, release it, and watch it oscillate in SHM as in (Figure 2). Find the following quantities: The force constant of the spring The maximum and minimum velocities attained by the vibrating object The maximum and minimum accelerations The velocity and acceleration when the object has moved halfway to the center from its initial position The kinetic energy, potential energy, and total energy in the halfway position
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
Let’s begin with a straightforward example of
- The force constant of the spring
- The maximum and minimum velocities attained by the vibrating object
- The maximum and minimum accelerations
- The velocity and acceleration when the object has moved halfway to the center from its initial position
- The kinetic energy, potential energy, and total energy in the halfway position
If you had pulled the object out a distance of 0.056 mm before releasing it, how much kinetic energy would it have at the 0.021 mm mark?
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