Consider a driven damped oscillator with k = 32.0 N/m, m = 0.5 kg and b = 1Ns/m. The driving force is F(t)=F0 cos ωt with F0 = 10N and ω= 2ω0 where ω0 is the natural frequency of the oscillator. Find the solution with initial conditions x(t=0) = 2m and v(t=0) = 0. (Use the symbols to solve the problem and plug in the numbers at the end of your calculation. You need to solve a differential equation instead of using the result for the driven damped harmonic oscillator.
Consider a driven damped oscillator with k = 32.0 N/m, m = 0.5 kg and b = 1Ns/m. The driving force is F(t)=F0 cos ωt with F0 = 10N and ω= 2ω0 where ω0 is the natural frequency of the oscillator. Find the solution with initial conditions x(t=0) = 2m and v(t=0) = 0. (Use the symbols to solve the problem and plug in the numbers at the end of your calculation. You need to solve a differential equation instead of using the result for the driven damped harmonic oscillator.
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Consider a driven damped oscillator with k = 32.0 N/m, m = 0.5 kg and b = 1Ns/m. The driving force is F(t)=F0 cos ωt with F0 = 10N and ω= 2ω0 where ω0 is the natural frequency of the oscillator. Find the solution with initial conditions x(t=0) = 2m and v(t=0) = 0. (Use the symbols to solve the problem and plug in the numbers at the end of your calculation. You need to solve a differential equation instead of using the result for the driven damped harmonic oscillator.
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Step 1: Given data and to find:
VIEWStep 2: Equation of motion for the system
VIEWStep 3: Finding auxillary equation
VIEWStep 4: particular integral is calculated here
VIEWStep 5: Total solution written in the form of x(t)
VIEWStep 6: Initial conditions are used to find the value of constants
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