Establish the model for the y velocity of the needle as a function of time and the parameters A and w. Then test your model by calculating the speed in y of the needle at the moment and with the given parameters: Moment: 4.1 s Amplitude: 0.012 m Angular frequency: 17.9 rad/s
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.
Context
The needle of a sewing machine makes a repetitive up and down motion which is described by the equation
y(t)=Acos(wt)
To choose the settings of the device that will ensure that the needle successfully pierces the textile, you are asked to model the speed in y of the needle as a function of time.
Constraints and information
The parameter A represents the range of motion (in m);
The parameter w represents the angular frequency. It tells us about the number of back and forth movements that the needle makes per second;
The parameter w is given in rad/s, so your calculator absolutely must be in radians mode to do the calculations in this problem;
This type of movement is called Simple Harmonic Movement and will be studied in depth in the 3rd physics course
Modelization
Establish the model for the y velocity of the needle as a function of time and the parameters A and w.
Then test your model by calculating the speed in y of the needle at the moment and with the given parameters:
Moment: 4.1 s
Amplitude: 0.012 m
Angular frequency: 17.9 rad/s
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