e An undamped driven oscillator of mass m and natural frequency of oscillation wo is subjected...

 

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e An undamped driven oscillator of mass m and natural frequency of oscillation wo is subjected to an external force F(t) = F,cos²wt, where F, and ∞ (@#wo) are constants. The oscillator satisfies the following equation of motion mx +mw/x = F(t) Write down the general solution x₁ (t) to the corresponding homogeneous differential equation. (ii) Find the particular solution xp (t) to the above equation of motion. (iii) Determine the complete solution x(t) to the equation of motion using the initial conditions x (t = 0)=0, x (t=0) = 0. [5 Marks] e An undamped driven oscillator of mass m and natural frequency of oscillation wo is subjected to an external force F(t) = F,cos²wt, where F, and ∞ (@#wo) are constants. The oscillator satisfies the following equation of motion mx +mw/x = F(t) Write down the general solution x₁ (t) to the corresponding homogeneous differential equation. (ii) Find the particular solution xp (t) to the above equation of motion. (iii) Determine the complete solution x(t) to the equation of motion using the initial conditions x (t = 0)=0, x (t=0) = 0. [5 Marks] e An undamped driven oscillator of mass m and natural frequency of oscillation wo is subjected to an external force F(t) = F,cos²wt, where F, and ∞ (@#wo) are constants. The oscillator satisfies the following equation of motion mx +mw/x = F(t) Write down the general solution x₁ (t) to the corresponding homogeneous differential equation. (ii) Find the particular solution xp (t) to the above equation of motion. (iii) Determine the complete solution x(t) to the equation of motion using the initial conditions x (t = 0)=0, x (t=0) = 0. [5 Marks] e An undamped driven oscillator of mass m and natural frequency of oscillation wo is subjected to an external force F(t) = F,cos²wt, where F, and ∞ (@#wo) are constants. The oscillator satisfies the following equation of motion mx +mw/x = F(t) Write down the general solution x₁ (t) to the corresponding homogeneous differential equation. (ii) Find the particular solution xp (t) to the above equation of motion. (iii) Determine the complete solution x(t) to the equation of motion using the initial conditions x (t = 0)=0, x (t=0) = 0. [5 Marks]