A certain mass is supported by a spring such that it is at rest 1m above the ground. The mass is pulled up 0.5 m and released at t= 0, creating a periodic up and down motion called simple harmonic motion. It takes 1.8 seconds for the mass to return to its original position each time. O Draw a graph to show the height of the mass above the ground as a function of time for the first 5.4 seconds. -4)+c for b) Write an equation as a cosine function in the form h = ascos your graph in part (a). c) Use your equation to determine all the time(s) in the first 5 seconds where the height of the mass above the ground is 0.5 m. Full algebraic solution.
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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