Solving for Speed and Amplitude in Vibrating System
Understanding the Vibrating System
A small trailer and its load have a total mass of 250-kg. The trailer is supported by two springs, and the period of the oscillation is 0.8 s, leading to a natural frequency of 7.85 rad/sec.
Finding the Speed Causing Severe Vibration
The speed that will cause the most severe vibration can be calculated using the resonance frequency of the system. The total stiffness of the two springs can be determined using the natural frequency formula.
The amplitude of the trailer's vibration at a specific speed can be calculated using the equation for simple harmonic motion. The resonance frequency occurs when the oscillation frequency matches the natural frequency of the system, which is 7.85 rad/sec. The speed can be found using the speed formula of wavelength times frequency, with the given wavelength as 5 m.
Calculating Total Stiffness and Amplitude
To compute the total stiffness of the two springs, we use the formula for natural frequency and solve for stiffness. Since there are two springs, the total stiffness is the sum of individual spring stiffness. The amplitude at a speed of 50 km/h can then be found by calculating the displacement of the trailer using the equation for simple harmonic motion.
yz = 66 QUESTION 3 (continued) A small trailer and its load have a total mass of 250-kg. The trailer is supported by two springs, the period of the oscillation is 0.8 s (i.e. the natural frequency is 7.85 rad. How can we determine the speed that will cause the most severe vibration in the system? The speed that will cause the most severe vibration can be calculated by considering the resonance frequency, which occurs when the frequency of oscillation matches the natural frequency of the system. Given the natural frequency as 7.85 rad/sec, the speed can be determined using the speed formula of wavelength times frequency.