Assume an oscillator described by the following 2nd order DE: x" + 12x' + 100x = 0 where the displacement x is function of time r. 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).
Assume an oscillator described by the following 2nd order DE: x" + 12x' + 100x = 0 where the displacement x is function of time r. 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).
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Transcribed Image Text:Assume an oscillator described by the following 2nd order DE:
x" + 12x' + 100x = 0 where the displacement x is function of time t.
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 – 0); 0 must be
expressed in radians.
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