Figure 1 shows the features of a sinusoidal oscillatory motion. Write down the equa- tion of motion both in the form of a cosine and of a sine function. Make sure to include units for all parameters. For each of the two equations identify: • the amplitude A; • the frequency f; • the angular frequency w; • the phase constant o; • the phase ¢; • the period T. x[cm] 3 -2 -1 2 t[sec] -t -2 -3 Figure 1: Sinusoidal oscillatory motion.
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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Problem #1
Figure 1 shows the features of a sinusoidal oscillatory motion. Write down the
equa-
tion of motion both in the form of a cosine and of a sine function. Make sure to
include units for all parameters.
For each of the two equations identify:
• the amplitude A;
• the frequency f;
• the angular frequency w;
• the phase constant po;
• the phase o;
• the period T.
4 A
x[cm]
3
12
3
2
-1
1
t[sec}
-t
-2
-3
Figure 1: Sinusoidal oscillatory motion.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5dfcff76-5646-42a0-b45c-1f5ea8195891%2F062ed8a3-6160-4e9b-993a-a12e53f5a175%2Fvwac699_processed.png&w=3840&q=75)
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