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Figure 6 shows a boy sitting on a swing and being pumped (pushed) by a harmonic force Fosin⁡ωt where Fo is the force amplitude and ω is the angular frequency of pumping in the horizontal direction. This forced oscillation can be modelled by a simple pendulum which consists of a lumped mass m swinging at a distance L from the pivot. (i) Write the equation of motion for this pendulum under forced vibration. (ii) Find the amplitude of angular swing based on the assumption of a small angle. (7 marks) Figure 6

Figure 6 shows a boy sitting on a swing and being pumped (pushed) by a harmonic force Fosin⁡ωt where Fo is the force amplitude and ω is the angular frequency of pumping in the horizontal direction. This forced oscillation can be modelled by a simple pendulum which consists of a lumped mass m swinging at a distance L from the pivot. (i) Write the equation of motion for this pendulum under forced vibration. (ii) Find the amplitude of angular swing based on the assumption of a small angle. (7 marks) Figure 6

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Figure 6 shows a boy sitting on a swing and being pumped (pushed) by a harmonic force F o sin ⁡ ω t where F o is the force amplitude and ω is the angular frequency of pumping in the horizontal direction. This forced oscillation can be modelled by a simple pendulum which consists of a lumped mass m swinging at a distance L from the pivot. (i) Write the equation of motion for this pendulum under forced vibration. (ii) Find the amplitude of angular swing based on the assumption of a small angle. (7 marks) Figure 6

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