The force of a spring is given by F=−kx, where k is the stiffness of the spring and x is the displacement of the spring from equilibrium. From an earlier activity, we said that the derivative of the potential energy with respect to position is equal to the negative force. Assume that at quilibrium (when x= 0), the spring has no potential energy. (a) Write an initial value problem for solving PE(x). Clearly identify the initial condition. (b) Solve the initial value problem for the potential energy of the spring at position x. Clearly show the use of the initial condition to solve for the constant of integration. (c) How much potential energy is in the spring if it is stretched to x = 2 meters and the constant k= 20 Newtons/meter (include units)? (Note that 1 Joule = 1 Newton meter.)
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.
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