Question 5 The figure below shows a ballistic pendulum, which is used to measure the velocity of high-speed projectiles. A bullet of mass 20 grams and velocity vo is fired into a 5 kg wooden block B hanging off a massless string of length /= 2 m. The block then swings to a maximum angular displacement of ee = 10°. Vo (a) Determine the velocity of the bullet vo. (b) What percentage of the energy was dissipated after the impact? (c) What is the natural frequency of this pendulum in hertz? (d) If the fundamental resonant frequency is 5% less than the natural frequency, what is the damping ratio 33? Is this system over-damped, under-damped or critically damped? (e) If the pendulum was to be driven into its fundamental resonance outlined in part (d), what is the phase angle o in this scenario?

Question 5 The figure below shows a ballistic pendulum, which is used to measure the velocity of high-speed projectiles. A bullet of mass 20 grams and velocity vo is fired into a 5 kg wooden block B hanging off a massless string of length /= 2 m. The block then swings to a maximum angular displacement of ee = 10°. Vo (a) Determine the velocity of the bullet vo. (b) What percentage of the energy was dissipated after the impact? (c) What is the natural frequency of this pendulum in hertz? (d) If the fundamental resonant frequency is 5% less than the natural frequency, what is the damping ratio 33? Is this system over-damped, under-damped or critically damped? (e) If the pendulum was to be driven into its fundamental resonance outlined in part (d), what is the phase angle o in this scenario?