Aweight is attached to a spring and is suspended from a ceiling so that it lies 30 cm from the ceiling when it is at rest. The spring is stretched so that the weight is 38 cm from the ceiling and is then released. It bounces up and down for a while. Each time it comes to the bottom of its bounce, the length of the stretch is 75% of the previous stretch. a) The period of each oscillation (bounce) is 1/2 second. Write an equation that represents the distance from the weight to the ceiling. b) Draw a graph of the function. c) Without doing any calculations, state the distance of the spring from the ceiling after 1 minute
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.
Aweight is attached to a spring and is suspended from a ceiling so that it lies 30 cm from the ceiling when it is at rest. The spring is stretched so that the weight is 38 cm from the ceiling and is then released. It bounces up and down for a while. Each time it comes to the bottom of its bounce, the length of the stretch is 75% of the previous stretch.
a) The period of each oscillation (bounce) is 1/2 second. Write an equation that represents the distance from the weight to the ceiling.
b) Draw a graph of the function.
c) Without doing any calculations, state the distance of the spring from the ceiling after 1 minute
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