mass is supported by a spring so that it rests 50 cm above a tabletop, as shown in the diagram below. The mass is pulled down to a height of 40 cm above the tabletop and released at time t =0. It takes 0.8 seconds for the mass to reach a maximum height of 60 cm above the tabletop. As the mass moves up and down, its height h, in cm, above the tabletop, is approximated by a sinusoidal function of the elapsed time t, in seconds, for a short period of time. Determine an equation for a sine wave function that gives h as a function of t. (Draw a neatly labelled picture to support your answer.)
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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