1. An undamped harmonic oscillator of mass m and spring constant k oscillates with an amplitude A. In terms of A, at what postion x is the speed of the oscillator, v, is half of its maximum speed v max Think & Prepare 1. Set-up the mechanical energy equation at any postion in terms of the variables of m, k and A. In particular, set-up up two equations, one equation at x when v=Vmax/2 and one at x = A. 2. Is the mechanical energy conserved? If so, what how are the two energy equations in 1 related? 3. Solve for x when v=v, max/2 in term of the amplitude A. 4. How many solutions for x are there? x when vis 1 2max = +
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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