3: The questions vary with the student number. Each student has to solve the questions considering his or her student ID. X1(mm)=last number of your student ID yı(mm)=second to last number of your student ID y/y, 1.0 If any of them is zero, please take that value as five instead of zero. 0.5 The damped motion of a vibrating particle defined by the position vector x/x1 is 0.2 0.4 0.6 r= x1[1-1/(t+1)] i +(y;e™/?cos2nt) j -0.5 -1.0- where t is expressed in seconds. For x1 and x2, determine the position, the velocity, and the acceleration of the particle (with magnitudes and angles) when a) t=0 b) t=1.5 s X1=5 Y1=6
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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|3: The questions vary with the student number. Each
student has to solve the questions considering his or her
student ID.
y/y,
X1(mm)=last number of your student ID
y1(mm)=second to last number of your student ID
1.0
If any of them is zero, please take that value as five
instead of zero.
0.5
The damped motion of a vibrating particle
defined by the position vector
x/x1
is
0.2
0.4
0.6
r=xi[1-1/(t+1)] i+(yie™2cos2nt) j
–0.5
-1.0F
where t is expressed in seconds. For x1 and x2,
determine the position, the velocity, and the
acceleration of the particle (with magnitudes and
angles) when
a) t=0
b) t=1.5 s
X1=5
Y1=6](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e40ea8a-d173-46da-be7c-acf1bb284f5f%2F886464be-6d4d-4403-b6bc-2d819f65323f%2Fkusp67i_processed.png&w=3840&q=75)
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