a) Write an equation for distance from the floor as a function of time. b) Sketch a graph of this sinusoidal function. c) What is the distance from the floor when the stopwatch reads 17.2 seconds?
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.
![3. Bouncing Spring Problem: A weight attached to the end of a long spring is
bouncing up and down. As it bounces, its distance from the floor varies sinusoidally
with time. You start the stopwatch. When the stopwatch reads 0.3 seconds, the weight
first reaches a high point 60 centimeters above the floor. The next low point, 40
centimeters above the floor, occurs at 1.8 seconds.
a) Write an equation for distance from the floor as a function of time.
b) Sketch a graph of this sinusoidal function.
c) What is the distance from the floor when the stopwatch reads 17.2 seconds?
d) What was the distance from the floor when you started the stopwatch?
e) What are the first three positive values of time when the weight is 59 centimeters above the
floor?
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