Assume an oscillator described by the following 2nd order DE: x"+12x'+100x=0 where the displacement x is function of time t. 1 a) Find the general solution i.e. x(t).
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.
Assume an oscillator described by the following 2nd order DE:
x"+12x'+100x=0
where the displacement x is function of time t.
1 a) Find the general solution i.e. x(t).
b) Calculate the period of the oscillations; what would be the period of the same oscillator if the
motion was not damped?
c) Given that the initial position of the oscillator is 0.5 (SI units) away from equilibrium in the
+x direction and that its initial velocity is -10 (SI units); find the constants in the solution
obtained in a).
d) Write now your solution in Amplitude –phase form x(t)=Acos(wt-Q ); Q must be
expressed in radians
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